{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-variate Rregression Metamodel with DOE based on random sampling\n",
    "* Input variable space should be constructed using random sampling, not classical factorial DOE\n",
    "* Linear fit is often inadequate but higher-order polynomial fits often leads to overfitting i.e. learns spurious, flawed relationships between input and output\n",
    "* R-square fit can often be misleding measure in case of high-dimensional regression\n",
    "* Metamodel can be constructed by selectively discovering features (or their combination) which matter and shrinking other high-order terms towards zero\n",
    "\n",
    "#### LASSO: Least Absolute Shrinkage and Selection Operator\n",
    "$$ {\\displaystyle \\min _{\\beta _{0},\\beta }\\left\\{{\\frac {1}{N}}\\sum _{i=1}^{N}(y_{i}-\\beta _{0}-x_{i}^{T}\\beta )^{2}\\right\\}{\\text{ subject to }}\\sum _{j=1}^{p}|\\beta _{j}|\\leq t.} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random (equivalent to Latin Hypercube sampling done in Optislang) feature vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X=np.array(10*np.random.randn(37,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df=pd.DataFrame(X,columns=['Feature'+str(l) for l in range(1,6)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487\n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441\n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619\n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331\n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the random distributions of input features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAF6CAYAAADWCxt5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998dd2550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAF6CAYAAADWCxt5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMm8C53iXj0UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2299895dd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAF6CAYAAADWCxt5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQS1JUsMMakmSGmZQS5LUsP8Pq0abh+cVqvkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998e98908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAF6CAYAAADWCxt5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998b8ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAAF6CAYAAADWCxt5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUsMMakmSGvb/ARYm5kBZVLh7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998d76c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df.columns:\n",
    "    df.hist(i,bins=5,xlabelsize=15,ylabelsize=15,figsize=(8,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate the output variable by analytic function + Gaussian noise (our goal will be to *'learn'* this function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's construst the ground  truth  or  originating  function  as  follows: \n",
    " \n",
    "$$ y=f(x_1,x_2,x_3,x_4,x_5)= 5x_1^2+13x_2+0.1x_1x_3^2+2x_4x_5+0.1x_5^3+0.8x_1x_4x_5+\\psi(x)\\ :\\ \\psi(x) = {\\displaystyle f(x\\;|\\;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['y']=5*df['Feature1']**2+13*df['Feature2']+0.1*df['Feature3']**2*df['Feature1'] \\\n",
    "+2*df['Feature4']*df['Feature5']+0.1*df['Feature5']**3+0.8*df['Feature1']*df['Feature4']*df['Feature5'] \\\n",
    "+30*np.random.normal(loc=5,scale=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "      <td>-431.953540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "      <td>2072.648112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "      <td>1701.292666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "      <td>2253.726636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "      <td>486.519017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5            y\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487  -431.953540\n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441  2072.648112\n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619  1701.292666\n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331  2253.726636\n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401   486.519017"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot single-variable scatterplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAHntJREFUeJzt3X90XOV95/H3VwbLZiQCtolwZGGDpDR12JIEhXJ2tTki\npMGoDr8CGXf3FLfrjdPGTULcPQSaPScnbUgpOScpocDWx+TE6Sb1eClZFCOHpmyUVD1LwGSTgPkR\nSRD8Qw4udlJGYyxj67t/zLUZyyNpJN2re+fO53WOjq+eO/fOM48185n7PM88Y+6OiIhImOriroCI\niKSPwkVEREKncBERkdApXEREJHQKFxERCZ3CRUREQqdwERGR0ClcREQkdAoXEREJ3RlxVyAuS5Ys\n8RUrVkR2/kKhQCaTiez8aaK2qozaqTJqp8rMtJ2eeuqpV939vKluV7PhsmLFCnbu3BnZ+fv6+ujq\n6ors/GmitqqM2qkyaqfKzLSdzOzlSm6nbjEREQmdwkVEREKncBERkdApXEREJHQ1O6AvIjLX8vk8\nuVyOgcEB2tvayWazNDY2xl2tSChcRETmQH9/P93XdDPWMkZhSYHMjgwbb91Ib08vnZ2dcVcvdAoX\nEZGI5fN5uq/pJr86D63FsgIFGILua7oZ3j1MQ0NDvJUMmcZcREQilsvlGGsZOxksJ7XCWMsYuVwu\nlnpFSeEiIhKxgcEBCksKZfcVFhcYHBqc4xpFT+EiIhKx9rZ2Mq+WX2olczBDW2vbHNcoegoXEZGI\nZbNZ6vbUwdC4HUNQt6eObDYbS72ipAF9EZGINTY20tvT++ZsscUFMgcz1O2po7enN3WD+aBwERGZ\nE52dnQzvHiaXyzE4NEhbaxvZbDaVwQIKFxGROdPQ0MC6devirsac0JiLiIiETuEiIiKhU7iIiEjo\nFC4iIhI6hYuIiIRO4SIiIqFTuIiISOj0ORcRSaxa+nKttFG4iEgi1dqXa6WNwkVEEqcWv1wrbTTm\nIiKJU4tfrpU2ChcRSZxa/HKttIktXMxsgZk9YWY/NbNdZvb5oHyRmX3PzAaCf88tOeZ2Mxs0sxfM\n7KqS8kvN7Olg31fNzOJ4TCISjlr8cq20ifPKZRR4v7tfArwLWGVmlwO3AY+5ezvwWPA7ZrYSWAO8\nE1gF3Gdm84Jz3Q98FGgPflbN5QMRkXDV4pdrpU1s4eJFI8GvZwY/DlwLbAnKtwDXBdvXAlvdfdTd\nXwIGgcvMbClwtrs/7u4OfKPkGBGpQie+XKtxeyOZhzLwA8g8lKFxe2Nqv1wrbWKdLRZceTwFtAH3\nuvuPzKzJ3fcHN/kl0BRsNwOPlxy+Nyh7I9geXy4iVazWvlwrbWINF3c/DrzLzM4Bvm1mF4/b72bm\nYd2fma0H1gM0NTXR19cX1qlPMzIyEun500RtVZlabafW1lZaW4vTxnbu3Dnl7Wu1naYr6nZKxOdc\n3P3XZvZ9imMlr5jZUnffH3R5HQhutg9oKTlsWVC2L9geX17ufjYBmwA6Ojq8q6sr1MdRqq+vjyjP\nnyZqq8qonSqjdqpM1O0U52yx84IrFsxsIfA7wPNAD7A2uNla4OFguwdYY2b1ZnYhxYH7J4IutNfM\n7PJgltjNJceIiEgM4rxyWQpsCcZd6oBt7r7dzP4vsM3M1gEvAx8BcPddZrYNeBY4BmwIutUAPg58\nHVgI7Ah+REQkJrGFi7v/DHh3mfKDwJUTHHMHcEeZ8p3AxacfISIicdAn9EVEJHQKFxERCZ3CRURE\nQqdwERGR0ClcREQkdAoXEREJncJFRERCp3AREZHQKVxERCR0ChcREQmdwkVEREKncBERkdApXERE\nJHQKFxERCZ3CRUREQqdwERGR0ClcREQkdAoXEREJncJFRERCp3AREZHQKVxERCR0Z8RdARERmRv5\nfJ5cLsfA4ADv7Xgv+XyexsbGSO5L4SIiUgP6+/vpvqabsZYxCksKfPmCL9O8vJnenl46OztDvz+F\ni4hIyuXzebqv6Sa/Og+txbKxc8fIry6WD+8epqGhIdT71JiLiEjK5XI5xlrGTgbLSa0w1jJGLpcL\n/T4VLiIiKTcwOEBhSaHsvsLiAoNDg6Hfp8JFRCTl2tvaybyaKbsvczBDW2tb6PepcBERSblsNkvd\nnjoYGrdjCOr21JHNZkO/Tw3oT0PpNL72tnay2Wxk0/hEJFq19HxubGykt6f3zdliiwvUnVdH4/Zi\nediD+aBwqdj4aXyZHRk23roxsml8IhKdWnw+d3Z2Mrx7mFwux+DQIC1vbYlkltgJCpcKlJvGV6AA\nQ0Q2jU9EolHLz+eGhgbWrVsHQF9fX6SPM7YxFzNrMbPvm9mzZrbLzD4VlC8ys++Z2UDw77klx9xu\nZoNm9oKZXVVSfqmZPR3s+6qZWZh1jWMan4hEQ8/nuRHngP4x4E/dfSVwObDBzFYCtwGPuXs78Fjw\nO8G+NcA7gVXAfWY2LzjX/cBHgfbgZ1WYFY1jGp+IREPP57kRW7i4+353/3GwnQeeA5qBa4Etwc22\nANcF29cCW9191N1fAgaBy8xsKXC2uz/u7g58o+SYUMQxjU9EoqHn89xIxFRkM1sBvBv4EdDk7vuD\nXb8EmoLtZmBPyWF7g7LmYHt8eWjimMYnItHQ83luWPHNfowVMGsAfgDc4e4Pmdmv3f2ckv2/cvdz\nzexvgMfd/X8G5Q8AO4BfAHe6+weC8v8IfMbdV5e5r/XAeoCmpqZLt27dWnE9R0ZGGBgcgPkwdsYY\ndcfq4GjxXVC5QbGRkZHUDgqGTW1VGbVTZSppp+k+n9Nopn9PV1xxxVPu3jHV7WKdLWZmZwL/AHzT\n3R8Kil8xs6Xuvj/o8joQlO8DWkoOXxaU7Qu2x5efxt03AZsAOjo6vKura1r1HRkZOTmNr621jezN\n2Qn/c/r6+pju+WuV2qoyaqfKVNpO03k+p1HUf0+xhUswo+sB4Dl3/3LJrh5gLXBn8O/DJeXfMrMv\nA2+jOHD/hLsfN7PXzOxyit1qNwP3RFHn0ml8IlLd9HyOVpxXLv8B+H3gaTP7SVD2ZxRDZZuZrQNe\nBj4C4O67zGwb8CzFmWYb3P14cNzHga8DCyl2le2YqwchIiKniy1c3L0fmOjzKFdOcMwdwB1lyncC\nF4dXOxERmY1EzBYTEZF0UbiIiEjoFC4iIhI6LVwpIjIDtbRk/0woXEREpqkWl+yfLoWLiMg01PKS\n/dOhMRcRkWnQkv2VUbiIiEyDluyvjMJFRGQatGR/ZRQuIiLToCX7K6MBfRGRaWhsbKS3p/fN2WKL\nC2QOZqjbU0dvT68G8wMKFxGRaers7GR49/CpS/Zna2vJ/qkoXEREZkBL9k9OYy4iIhI6hYuIiIRO\n4SIiIqFTuIiISOg0oC+JppVnRaqTwkUSSyvPilQvhYskklaeFaluGnORRNLKsyLVTeEiiaSVZ0Wq\nm8JFEkkrz4pUN4WLJJJWnhWpbhrQl0TSyrMi1U3hIomllWdFqpfCRRJNK8+KVCeNuYiISOgULiIi\nEjqFi4iIhG7KcDGzT5jZuXNRGRERSYdKrlyagCfNbJuZrTIzC+vOzexrZnbAzJ4pKVtkZt8zs4Hg\n33NL9t1uZoNm9oKZXVVSfqmZPR3s+2qYdZSifD7P5s2b+cxtn2Hz5s3k8/m4qyQiCTZluLj7fwfa\ngQeAPwAGzOyLZjZ+1aeZ+DqwalzZbcBj7t4OPBb8jpmtBNYA7wyOuc/M5gXH3A98NKhne5lzyiz0\n9/fTvLyZW+65hbuevItb7rmF5uXN9Pf3x101EUmoisZc3N2BXwY/x4BzgQfN7K7Z3Lm7/xA4NK74\nWmBLsL0FuK6kfKu7j7r7S8AgcJmZLQXOdvfHg3p+o+QYmaXS1YkLNxTgfVC4oUB+dbF8ZGQk7iqK\nSAJVMubyKTN7CrgL+Bfg37n7HwOXAh+OoE5N7r4/2P4lxW45gGZgT8nt9gZlzcH2+HIJgVYnFpGZ\nqORDlIuAG9z95dJCdx8zs9XRVOvkfbiZeVjnM7P1wHqApqYm+vr6wjr1aUZGRiI9/1xZuHAhn9/w\neSj35Y8bYMGCBbN+nGlpq6ipnSqjdqpM1O00Zbi4++cm2fdcuNUB4BUzW+ru+4MurwNB+T6gpeR2\ny4KyfcH2+PJy9d0EbALo6Ojwrq6ukKv+pr6+PqI8/1zZvHkzn7v3c8UusXEyD2W4+5N3z/pxpqWt\noqZ2qozaqTJRt1MSP+fSA6wNttcCD5eUrzGzejO7kOLA/RNBF9prZnZ5MEvs5pJjZJa0OrHI6TR7\ncmqxri1mZn8PdAFLzGwv8DngTmCbma0DXgY+AuDuu8xsG/AsxUkFG9z9eHCqj1OcebYQ2BH8SAi0\nOrHIqfr7+998PiwpkNmRYeOtG+nt6aWzszPu6iVGrOHi7r83wa4rJ7j9HcAdZcp3AheHWDUpodWJ\nRYpKZ0+emORSoABD0H1NN8O7h/W8CGhVZKmIVicWqWz2pJ4nRUkccxERSaSBwQEKS06f3AJQWFxg\ncGhwjmuUXAoXEZEKtbe1k3k1U3Zf5mCGtta2Oa5RcilcUkwzWkTCpdmTldOYS0ppRotI+DR7snIK\nlxSq1hkt+XyeLVu2sP2R7WCwuns1a9eupbGx3PIAIvGodPZkPp8nl8sxMDhAe1s72Wy2pv6WFS4p\nVI0zWvr7+/lg9wd5ffR1WAEsg0f/+lE+89nP8Ogjj+pqSxJlqtmT6jlQuKRStc1oGRsb4+oPXc3r\nx16HLKeE4uGhw1z9oavZv2f/hFdbtf4OUZKlWnsOwqZwSaH2tnYyOzLFP+hxkjij5dChQxzNHIXz\nKXu19cbb3pjwamuid4gPbn2Q3bt3K3BkzlVjz0EUFC4plM1m2XjrxuKMltI/8ITOaBkdHeXoGUfh\nbRPsbxote7U12TvEq1ZfxVlvP4vDTYdrskuiGqT1irPaeg6ionBJoWqb0VJfX8/8Y/M5Ony0/P5X\n6stebU32DpEL4XDrYXhPbXZJJF2axySqrecgKgqXlKqm9cAWLVrE/MJ8jh46WvZq68zhM8tebU32\nDpFm4Fclv0/SJZHWd9BJlfYxiWrrOYiKwiUFJnpxrJb1wOrq6tjxnR3F2WK512E5xW/l2Q1n/etZ\n7HhkR9kXm8neIbIfePupReW6JNL8Djqp0j4mUW09B1FRuFS5tLw4dnZ2cmD4AFu2bOGR3kcA+N1P\n/y5r166d8Mk42TtEdgPXn3r78V0SaX8HnVS1MCZRTT0HUVG4VLG0vTg2NDSwYcMGNmzYUNHty71D\nPOvgWRx+7jC8H6gvuXGZLom0v4NOqloZk6iWnoOoKFyqmF4cy79DbGlp4cY1NzK2f/IuiVp4B51E\nSRiT0Dhb9BQuVUwvjkXl3iGWBs6y5mW4O9/Z/h2ef/75ky8kSXsHXSsveHGPSaSlKznpFC5VLGkv\njklyInAmeyFJwjvoE2rtBS+uMYm0dSUnmcKliiXpxTGJKnkhScKsnlp9wYtjTEJdyXNH4VLF4u5e\niEKYXUOVvpDEPatHL3hzJ8qu5Frp1qyUwqXKpWnKY9hdQ5W+kMQ9q0djZ3Mnqq7kWuvWrITCJQXi\nfnEMQxRdQ9UyJlUt9UyDKLqSa7Vbcyr6mmNJhEq6hip14uudn9n1DMdfPJ74r6Tt7u6uinqmwYmu\n5MbtjWQeysAPIPNQhsbtjTPuSg7zbzdNdOUiiRBW19D47okFTQtgKyx4+wKOvPVI4sakTtSXJmAb\ncAGwDBYcWMCZw2cmpp5pEnZXsro1y1O4SCKE0TVUrnviCEfgefAeZ+Oqjaz8zZXTeiGJcpB2eHiY\nD1z1AUYvGoULgWuBQeBF8Jecnw/9nPPPPz+U+5JThdmVrG7N8tQtJomQzWap21M3q66hCbsn3gFn\ntJ3Byt9cybp16yoOlv7+fpqXN3PLPbdw15N3ccs9t9C8vJn+/v7KHtQU5279jVZGm0fhrcAA8D+A\nxcCNxfo+8sgjs74fiV4Yf7tppCsXSYQwplWH2T0R5SDtiXMfuf7I6Qtu5oBPFeu769ldbN68+eRV\n00UXXTTt+9HU2Oil8SMBYVC4SGLMti88zO6JKD97MumXnF0A7IIFuxdw/5P3M++ieSentv7FH/4F\n8+fPr2hqq6bGzq00fSQgLAoXSZTZ9IWHOc00ykHaSb/kbCkwAEd2H4E1nHLVNHbO2MmrJnef8KpE\nU2PjkYaPBIRJYy6SGmFOM21vayfzaqbsvtkO0k52bvbCGUNnsODtC06/sqkvXjV94QtfmHQsSFNj\nJQkULpIqJ7on7v7k3dx2+W3c/cm7Gd49PO2uoCgHaSc794L9C/jY+o9xpOlI2WMLbynwlXu+Qn51\nnsINBXgfFG4okF9dvFoZGRnR1FhJhNR0i5nZKuBuYB6w2d3vjLlKEpMwuieiHKSd9Nw7enn++efJ\n/LD82NH8F+djK6zsVcnxluNs2LCBVw68Qv3+ekYZPe34Wp4aK3MrFeFiZvOAe4HfAfYCT5pZj7s/\nG2/NpJpFOUg72bkvueSS8mNHo+CHnKO/cbTsOQ8vPsy3vvstjr3jWPFYrZYtMUpFuACXAYPu/iKA\nmW2l+JE0hYvMSpSDtBOde8Irmz+s49Of+DT3fvfeslc17INjlx+D91AMla3A24ALCH1qrKY5y1TM\n3eOuw6yZ2Y3AKnf/r8Hvvw/8trv/ybjbrQfWAzQ1NV26devWyOo0MjKiGTkVUluVNzY2xqFDhxgd\nHaW+vp76+noymQw//dlPGTtnDOpLbjwK/IriBzJPjKSOgR0yzl54Nueccw6LFi2irm72w6wnxnWY\nD2NnjFF3rA6OFicqJOH/UX9PlZlpO11xxRVPuXvHVLdLy5VLRdx9E7AJoKOjw7u6uiK7r76+PqI8\nf5qorSpzop3mz5/P1R+6mjeWvsHo+aPM2zeP4y8fh/8ELB930A/gtstv4y+/+Jeh1CGfz9O8vPmU\nac4ADEHjnzcmYpqz/p4qE3U7pWW22D6gpeT3ZUGZSGp53uFFsLzBWPnbhD2Ar2nOUqm0XLk8CbSb\n2YUUQ2UNxfdxIpGJY9zhxAckRz40cvIF/hjBAP5W4Bbe7C6LYABf05ylUqkIF3c/ZmZ/AjxKcSry\n19x9V8zVkhSLa3mVSZeOeRvM/7v5HG0/GtnaVloBWCqVinABcPdeoDfuekj6xbm8yqRLx1wAVy68\nkksuuSSyta2i+CZHSafUhIvIXIlyUcupTHXl8OFPfjjS9a20ArBUSuEiMk1xjjsk4cpBKwBLJRQu\nItMU57hDUq4ctAKwTEXhIjJNcV896MpBqoHCRWSaknD1oCsHSTqFi8gM6OpBZHIKF5EZ0tWDyMQU\nLimlVWtFJE4KlxSK69PjIiInKFxSJs5Pj4uInJCWVZEloFVrRSQJFC4po1VrRSQJFC4p097WTubV\nTNl9WrVWROaKwiVlstksdXvqip8eL6VVa0VkDmlAP2WS8OlxERGFSwrp0+MiEjeFS0rp0+MiEieN\nuYiISOgULiIiEjqFi4iIhE7hIiIioVO4iIhI6BQuIiISOoWLiIiETuEiIiKhU7iIiEjoFC4iIhI6\nhYuIiIRO4SIiIqFTuIiISOhiCRczu8nMdpnZmJl1jNt3u5kNmtkLZnZVSfmlZvZ0sO+rZmZBeb2Z\n5YLyH5nZirl9NCIiMl5cVy7PADcAPywtNLOVwBrgncAq4D4zmxfsvh/4KNAe/KwKytcBv3L3NuAr\nwF9FXnsREZlULOHi7s+5+wtldl0LbHX3UXd/CRgELjOzpcDZ7v64uzvwDeC6kmO2BNsPAleeuKoR\nEZF4JO3LwpqBx0t+3xuUvRFsjy8/ccweAHc/Zmb/BiwGXo28tiIyp/L5PLlcjoHBAdrb2slmszQ2\nNsZdLSkjsnAxs38Czi+z67Pu/nBU9zsZM1sPrAdoamqir68vsvsaGRmJ9PxporaqTK2308jICAOD\nAzAf3nrRW8kfzbP5gc20t7Wf8hXetd5OlYq6nSILF3f/wAwO2we0lPy+LCjbF2yPLy89Zq+ZnQG8\nBTg4QZ02AZsAOjo6vKurawZVrExfXx9Rnj9N1FaVqeV2yufzNC9vJr86D60lO4ag8c8bGd49fDJg\narmdpiPqdkraVOQeYE0wA+xCigP3T7j7fuA1M7s8GE+5GXi45Ji1wfaNwP8JxmVEJCVyuRxjLWOn\nBgtAK4y1jJHL5WKpl0wsljEXM7seuAc4D3jEzH7i7le5+y4z2wY8CxwDNrj78eCwjwNfBxYCO4If\ngAeAvzOzQeAQxdlmIpIiA4MDFJYUyu4rLC4wODQ4xzWSqcQSLu7+beDbE+y7A7ijTPlO4OIy5UeA\nm8Kuo4gkR3tbO5kdGQqcHjCZgxnaWttiqJVMJmndYiIip8lms9TtqYOhcTuGoG5PHdlsNpZ6ycSS\nNhVZROQ0jY2N9Pb00n1NN2MtYxQWF8gczFC3p47ent5TZotJMihcRKQqdHZ2Mrx7mFwux+DQIG2t\nbWSzWQVLQilcRKRqNDQ0sG7durirIRXQmIuIiIRO4SIiIqFTuIiISOgULiIiEjoN6IvIpLQSscyE\nwkVEJtTf3//mZ0uWFMjsyLDx1o309vTS2dkZd/UkwRQuIlJWPp+n+5ruU1YiLlCAIei+pvuUlYhF\nxtOYi4iUpZWIZTYULiJSllYiltlQuIhIWe1t7WRezZTdp5WIZSoKFxEpSysRy2xoQF9EytJKxDIb\nChcRmZBWIpaZUriIyKS0ErHMhMZcREQkdAoXEREJncJFRERCp3AREZHQmbvHXYdYmNm/Ai9HeBdL\ngFcjPH+aqK0qo3aqjNqpMjNtp+Xuft5UN6rZcImame10946461EN1FaVUTtVRu1UmajbSd1iIiIS\nOoWLiIiETuESnU1xV6CKqK0qo3aqjNqpMpG2k8ZcREQkdLpyERGR0ClcQmZmXzKz583sZ2b2bTM7\np2Tf7WY2aGYvmNlVcdYzbmZ2k5ntMrMxM+sYt0/tVMLMVgVtMWhmt8VdnyQxs6+Z2QEze6akbJGZ\nfc/MBoJ/z42zjklgZi1m9n0zezZ43n0qKI+srRQu4fsecLG7/xbwc+B2ADNbCawB3gmsAu4zs3mx\n1TJ+zwA3AD8sLVQ7nSp47PcCVwMrgd8L2kiKvk7x76TUbcBj7t4OPBb8XuuOAX/q7iuBy4ENwd9R\nZG2lcAmZu/+jux8Lfn0cWBZsXwtsdfdRd38JGAQui6OOSeDuz7n7C2V2qZ1OdRkw6O4vuvtRYCvF\nNhLA3X8IHBpXfC2wJdjeAlw3p5VKIHff7+4/DrbzwHNAMxG2lcIlWv8F2BFsNwN7SvbtDcrkVGqn\nU6k9pq/J3fcH278EmuKsTNKY2Qrg3cCPiLCt9H0uM2Bm/wScX2bXZ9394eA2n6V4KfrNuaxbklTS\nTiJRcnc3M02JDZhZA/APwC3u/pqZndwXdlspXGbA3T8w2X4z+wNgNXClvznXex/QUnKzZUFZak3V\nThOouXaagtpj+l4xs6Xuvt/MlgIH4q5QEpjZmRSD5Zvu/lBQHFlbqVssZGa2CrgVuMbdD5fs6gHW\nmFm9mV0ItANPxFHHhFM7nepJoN3MLjSz+RQnO/TEXKek6wHWBttrgZq/SrbiJcoDwHPu/uWSXZG1\nlT5EGTIzGwTqgYNB0ePu/kfBvs9SHIc5RvGydEf5s6SfmV0P3AOcB/wa+Im7XxXsUzuVMLNu4K+B\necDX3P2OmKuUGGb290AXxRV+XwE+B/xvYBtwAcWVzz/i7uMH/WuKmXUC/ww8DYwFxX9GcdwlkrZS\nuIiISOjULSYiIqFTuIiISOgULiIiEjqFi4iIhE7hIiIioVO4iMyCmR03s5+U/KyYwTnOMbOPh1yv\n95nZj83smJndGOa5RSqhqcgis2BmI+7eMMtzrAC2u/vF0zxunrsfn+ScZwP/Dehx9wdnU0eR6dKV\ni0jIzGxe8L0+Twbf6/OxoLzBzB4LriieNrMTqxvfCbQGVz5fMrMuM9tecr6/CZYUwsx+YWZ/ZWY/\nBm4ys1Yz+66ZPWVm/2xm7wBw91+4+8948wNzInNKa4uJzM5CM/tJsP2Su18PrAP+zd3fa2b1wL+Y\n2T9SXN34+mDBwCXA42bWQ/E7NC5293cBmFnXFPd50N3fE9z2MeCP3H3AzH4buA94f9gPUmS6FC4i\ns/P6iVAo8UHgt0rGOt5CcY20vcAXzex9FK8ompnZEuc5OLnC7b8H/lfJ6rb1MzifSOgULiLhM+AT\n7v7oKYXFrq3zgEvd/Q0z+wWwoMzxxzi1y3r8bQrBv3XAr8uEm0jsNOYiEr5HgT8OljjHzN5uZhmK\nVzAHgmC5Alge3D4PNJYc/zKwMlgZ+hzgynJ34u6vAS+Z2U3B/ZiZXRLNQxKZHoWLSPg2A88CPzaz\nZ4C/pdhL8E2gw8yeBm4Gngdw94MUx2WeMbMvufseiivVPhP8+/8mua//DKwzs58Cuwi+AtnM3mtm\ne4GbgL81s10RPE6RCWkqsoiIhE5XLiIiEjqFi4iIhE7hIiIioVO4iIhI6BQuIiISOoWLiIiETuEi\nIiKhU7iIiEjo/j9Af/hleNgpbQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998c88a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAH6tJREFUeJzt3X90XOWd3/H3d0ws6EgJNgLFlRVsLJEt0LCJXdbbKqy9\npIvRIYaQH0O6XdjWjduETcJxc0A02SYhJSFkS4+TbLIhJhuym12Pu0uKS+SwCbGSak8JGMpv8GoU\ngmVsQm3DMppsBWa+/WOu7EEejUYzd+bemfm8zpmjq+fOnfnq6s58732e5z6PuTsiIiJhSkQdgIiI\ntB4lFxERCZ2Si4iIhE7JRUREQqfkIiIioVNyERGR0Cm5iIhI6JRcREQkdEouIiISupOiDiAq3d3d\nvmLFippeI5fLkUwmwwkoZIqtOoqtenGOT7FVp1RsDz744CF3P33ejd29LR+rV6/2Wu3evbvm16gX\nxVYdxVa9OMen2KpTKjZgj1fwHatqMRERCZ2Si4iIhE7JRUREQqfkIiIioWvb3mLVyGazpNNpxjPj\nDPQPcNZZZ0UdkohILCm5VGhsbIyhjUPk+/LkunMkdyX53L/5HIsXL2ZwcDDq8EREYkXJpQLZbJah\njUNkL83CqkJZjhz5U/MMbRziwL4DdHZ2RhukiEiMqM2lAul0mnxf/lhiOaYD8n150ul0JHGJiMSV\nkksFxjPj5LpzJdflTsuRmcg0OCIRkXhTcqnAQP8AyUOlh2dIHk7Sv6q/wRGJiMSbkksFUqkUickE\nTMxaMQ2JyQSpVCqSuERE4krJpQJdXV2M7Byh6+4ukncm4SeQvDNJ4qUEIztH1JgvIjKLeotVaHBw\nkAP7DpBOp8lMZOhf1c/KlSvVDVlEpAQllwXo7Oxk06ZNx34fHR2NLhgRkRhTtZiIiIROyUVEREKn\n5CIiIqFTchERkdApuYiISOiUXEREJHRKLiIiEjrd5yIyj9mTxKVSKbq6uqIOSyTWlFxEyig1SdyW\n67YwsnNEozOIlKHkIjKHuSaJYwJNEicyD7W5iMxhzkniVmmSOJH5KLmIzEGTxIlUL7LkYmYnm9n9\nZvaImT1hZp8Nypea2Q/NbDz4uaRomxvMLGNme83s4qLy1Wb2WLDuy2ZmUfxN0lo0SZxI9aK8cpkG\nftvdzwd+HdhgZmuBYeBedx8A7g1+x8zOAa4EzgU2AF8zs0XBa30d+BAwEDw2NPIPkdY05yRxE5ok\nTmQ+kSUXL5gKfn1D8HDgMuCOoPwO4PJg+TJgu7tPu/szQAa4wMyWAW909/vc3YHvFG0jUrW5Jonr\nurtLk8SJzCPS3mLBlceDQD/wx+7+MzPrcfeDwVOeB3qC5V7gvqLN9wdlrwbLs8tFalZqkrhUKqXE\nIjIPK5zsRxyE2anA94CPAmPufmrRuhfdfYmZfRW4z93/PCi/HdgF/AK42d3fFZS/E7je3S8t8T6b\ngc0APT09q7dv315T3FNTU7H9klFs1VFs1YtzfIqtOqViW79+/YPuvmbejd09Fg/gPwOfAPYCy4Ky\nZcDeYPkG4Iai598D/GbwnKeLyj8IfGO+91u9erXXavfu3TW/Rr0otuooturFOT7FVp1SsQF7vILv\n9Ch7i50eXLFgZqcA/xJ4GtgJXB087WrgrmB5J3ClmXWY2UoKDff3e6EK7WUzWxv0EruqaBsREYlA\nlG0uy4A7gnaXBLDD3e82s/8N7DCzTcCzwAcA3P0JM9sBPAkcBa5x99eC1/oI8G3gFApVZbsa+peI\niMjrRJZc3P1R4O0lyg8DF82xzU3ATSXK9wDnhR2jiIhUR3foi4hI6JRcREQkdEouIiISOiUXEREJ\nnZKLiIiETslFRERCp+QiIiKhU3IREZHQKbmIiEjolFxERCR0Si4iIhI6JRcREQmdkouIiIROyUVE\nREKn5CIiIqFTchERkdApuYiISOiUXEREJHRKLiIiEjolFxERCZ2Si4iIhO6kqAMQEYlKNpslnU4z\nnhlnoH+AVCpFV1dX1GG1BCUXEWlLY2NjDG0cIt+XJ9edI7kryZbrtjCyc4TBwcGow2t6Si4i0nay\n2SxDG4fIXpqFVYWyHDmYgKGNQxzYd4DOzs5og2xyanMRkbaTTqfJ9+WPJZZjVkG+L086nY4krlai\n5CIibWc8M06uO1dyXe60HJmJTIMjaj1KLiLSdgb6B0geSpZclzycpH9Vf4Mjaj1KLiLSdlKpFInJ\nBEzMWjEBickEqVQqkrhaiRr0pSJzddlUV05pRl1dXYzsHDneW+y0HMnDSRKTCUZ2jqgxPwRKLjKv\nubps3vxfbmb4U8PqyilNaXBwkAP7DpBOp8lMZOhf1U8qlVJiCYmSi5RVrsvmNddeA+8Ffu315erK\nKc2is7OTTZs2RR1GS4qszcXM+sxst5k9aWZPmNnHg/KlZvZDMxsPfi4p2uYGM8uY2V4zu7iofLWZ\nPRas+7KZWRR/Uysq12WTFcCvTixXV04RibJB/yjwH939HGAtcI2ZnQMMA/e6+wBwb/A7wborgXOB\nDcDXzGxR8FpfBz4EDASPDY38Q1pZuS6bLAdePLFYXTlFJLLk4u4H3f2hYDkLPAX0ApcBdwRPuwO4\nPFi+DNju7tPu/gyQAS4ws2XAG939Pnd34DtF20iNynXZZD+w5MRideUUkVh0RTazFcDbgZ8BPe5+\nMFj1PNATLPcCk0Wb7Q/KeoPl2eUSgnJdNvkF8I9OLFdXThGxwsl+hAGYdQI/AW5y9zvN7CV3P7Vo\n/YvuvsTMvgrc5+5/HpTfDuyi8BV3s7u/Kyh/J3C9u19a4r02A5sBenp6Vm/fvr2m2KempmLbaB1m\nbFNTU4xnxmEx5E/KkziagFdgee9y9j+3/4Tygf6Bsu/dLvstbHGODeIdn2KrTqnY1q9f/6C7r5lv\n20h7i5nZG4C/Br7r7ncGxb80s2XufjCo8nohKH8O6CvafHlQ9lywPLv8BO5+G3AbwJo1a3zdunU1\nxT86Okqtr1EvYcc2NTX1+i6bVxW6bM5V3sjYwqTYqhfn+BRbdWqJLbLkEvTouh14yt1vLVq1E7ga\nuDn4eVdR+V+Y2a3AP6bQcH+/u79mZi+b2VoK1WpXAV9p0J/RNubqsqmunCJSSpRXLv8C+D3gMTN7\nOCj7TxSSyg4z2wQ8C3wAwN2fMLMdwJMUeppd4+6vBdt9BPg2cAqFqrJdjfojRETkRJElF3cfA+a6\nH+WiOba5CbipRPke4LzwohMRkVrEoreYiIi0FiUXEREJnZKLiIiETgNXikjkNHVD61FyEZFIzTWl\ng6ZuaG5KLiISmXJTOmjqhuamNhcRiUy5KR00dUNzU3IRkciUm9JBUzc0NyUXEYlMuSkdNHVDc1Ny\nEZHIlJvSQVM3NDc16ItIZLq6uhjZOXK8t9hpOZKHkyQmE4zsHFFjfhNTchGRSA0ODnJg34HXT92Q\nmn/qBok3JRcRiZymbmg9anMREZHQKbmIiEjolFxERCR0Si4iIhI6NeiLlKHRekWqo+QiMgeN1itS\nPSUXkRI0Wq9IbdTmIlKCRusVqY2Si0gJGq1XpDZKLiIlaLRekdoouYiUoNF6RWqjBn2REjRar0ht\nlFxE5qDRekWqp+QiUoZG6xWpjtpcREQkdEouIiISOiUXEREJ3bzJxcw+amZLGhGMiIi0hkquXHqA\nB8xsh5ltMDML683N7Ftm9oKZPV5UttTMfmhm48HPJUXrbjCzjJntNbOLi8pXm9ljwbovhxmjiDSH\nbDbLtm3buH74erZt20Y2m406pLY2b3Jx908BA8DtwO8D42b2eTObPepSNb4NbJhVNgzc6+4DwL3B\n75jZOcCVwLnBNl8zs0XBNl8HPhTEOVDiNUWkhY2NjdF7Zi/XfuVabnngFq79yrX0ntnL2NhY1KG1\nrYraXNzdgeeDx1FgCfBXZnZLLW/u7j8Fjswqvgy4I1i+A7i8qHy7u0+7+zNABrjAzJYBb3T3+4I4\nv1O0jYi0uOIRrHNX5OBCyF2RI3tpoXxqairqENtSJW0uHzezB4FbgL8F/qm7fxhYDby3DjH1uPvB\nYPl5CtVyAL3AZNHz9gdlvcHy7HIRaQMawTqeKrmJcilwhbs/W1zo7nkzu7Q+YR17DzczD+v1zGwz\nsBmgp6eH0dHRml5vamqq5teoF8VWHcVWvajiO+WUU/jsNZ+FUhOEXgMnn3xyrPddy8bm7pE+gBXA\n40W/7wWWBcvLgL3B8g3ADUXPuwf4zeA5TxeVfxD4xnzvu3r1aq/V7t27a36NelFs1VFs1Ysqvm9+\n85uefFvS+QwnPJJvS/q2bdtive+aLTZgj1fw3R7H+1x2AlcHy1cDdxWVX2lmHWa2kkLD/f1eqEJ7\n2czWBr3EriraRqSttGOPKY1gHU+Rji1mZn8JrAO6zWw/8GngZmCHmW0CngU+AODuT5jZDuBJCp0K\nrnH314KX+giFnmenALuCh0hbGRsbOz6Kc3eO5K4kW67bwsjOEQYHB6MOr240gnU8RZpc3P2Dc6y6\naI7n3wTcVKJ8D3BeiKGJNJXiHlMzDds5cjABQxuHOLDvQEt/yWoE6/jRqMgiLaCSHlOtPrqzRrCO\nlzi2uYjIAo1nxsl150quy52WIzORaXBE0u6UXERawED/AMlDyZLrkoeT9K/qb3BE0u6UXERqFIce\nWuoxJXGjNheRGsSlh5Z6TEncKLmIVCluPbSq6TGVzWZJp9OMZ8YZ6B8glUrR1VXqVvf6iUMM7aKR\n+1rJRaRKceyhtZAeU3G46opDDO2i0ftayUWkSs3cQ2uhV131OOON25VfK4tiX6tBX6RKzdxDayEj\nCddrrhSNZlydajqQRLGvlVxEAtlslkOHDlX8oW3mHlqVXnXVc66UZr7yi0q1iT6Kfa3kIsLxD+3k\nC5MVf2hnemh13d1F8s4k/ASSdybpursr9j20Kr3qqucZbzNf+UWhlkQfxb5WcpG2V/yhzS/JL+hD\nO9NDa+vHtjK8dpitH9vKgX0HYt8YXelVVz3PeJv5ym+2RtzrVEuij2Jfq0Ff2l6tvb6acUyrSu+L\nGegfILkrWWj8naXj+Q6W9y6vewxx16heWLUk+ij2tZKLtL12rfuv5L6YVCrFluu2FM54i5PvBExP\nTDP8qWHOP//8qr9Em30040b2wiqX6Cup2mr0vlZykbZX64e2mc131TVzxnvJuy9h6rQpeAtwENgH\n/C5MHZ069iVarxjirJH3OpVL9JVWbTVyX6vNRZpaGHXdrVT3Xw+Dg4N84XNfYPH04sI0fWcDHwfO\npO27DTfyqrfZOpDoykWaVlh13cX10Ym1icKHtgnr/utpcv8kr5z9Clx44rqZL9FVq2afvteukps3\noxw+ptFXvc1UjajkIk0p7LrumQ/tD37wA4bXDsf6QxuFKKoOKzl5iHr4mDCqqhaqWaoRlVykKdWj\nrruzs5Pu7m6+8PkvhBdoi6jkS3TPnj2hvV8lJw/uHvnwMa3S460elFykKUXZw6sdR/Ft9JdoJScP\n7r7gE4x6/O+aqaqqkZRcpClF1cMr6mqYKDXyS7SSk4d8Pr+gE4x6/u+apaqqkZRcpClFUdetUXwb\n9yVaycmDu1d8gpHP59v+f9do6oos84rDNL6zRdEtU6P4nqj42Dh06FBox0Yl3cMX0oX8yJEj+t81\nmK5cpKw4VwM1uq67Xe/kn8vsY+PWt9xK75m9oRwblbbxVNoOND09rf9dgym5yJyaoRqo2mqacg27\nc61r5zv5Zyt1bOSX5I8N9hnGsVHJyUOlJxgdHR0kD+l/10hKLjKnOE7jG4ZyV2NTU1P0ntlbcl0U\n7Txx1ahjo5KTh0qes3Tp0uNVaG3+v2sUJReZUytWA5W7Grvk3Zdw46dvLHulFpd7GurZHbqS1262\nYyORSMTmf9culFxkTq1YDVTujPvVZa/ii3zes/Go72moZztYpa/djMeG7kdpLCUXmVMrVgOVO+Oe\nfvM0jpdcV3w27u6FG/jy+WPLjVLPdrCFvHazHhu6H6Vx1BVZ5tRso7BWotx0rx3Pd2BYyXUzZ+PV\nzmEelnp2h17Ia5c6NhIvJpr62JBw6cpFymq1qoRyZ9xvOPgG7DWb82x8aGiIt5771kh7z9WzrWOh\nrz372Og7oy8WPQglHlomuZjZBmArsAjY5u43RxxSy2ilqoSy90/8zxFeeuklum7sKtno+/3vfz/y\n3nP1bOuo5rWLj43R0dFYJpZsNsuhQ4e4fvj6thkLLg5aolrMzBYBfwxcApwDfNDMzok2KomrmTPu\nrR/byvDaYbZ+bCsH9h1gcHCQzs7OOdfFoYdUPSc2a8VJ02aqMSdfmIykGrOdtcqVywVAxt1/DmBm\n24HLgCcjjUpCE3bX23JXY3Oti0MPqXqOTtxqw8cXd1DIL8nDhfG7CbiVWSN7utSLmb0P2ODu/y74\n/feA33D3P5j1vM3AZoCenp7V27dvr+l9p6amYntwtlJsU1NTjGfGYTHkT8qTOJqAVwpf9mH/jeVi\ny+fzPPLoI+RPzUNH0YppSLyU4Py3nU8iUb/KgOLY8vk8R44cYXp6mo6OjsJNgiG9d7WvHbdj7tCh\nQ0y+MEl+SZ7lHcvZP73/2LrEiwn6zuiju7s7wggL4rbfipWKbf369Q+6+5r5tm2VK5eKuPttwG0A\na9as8XXr1tX0ej/+8Y/JZDKxnNdjdHSUWv++ellIbNlslt4ze1/XiA7ABHTd2BX62ed8sS1evHjO\nM/t6j7UW5/8pxC++64ev55YHboEL4Y/O/iM+8XefOL7yJzC8djgWE8PFbb8VqyW2VkkuzwF9Rb8v\nD8rqZmxsjEcefYQ//NM/jN2Ajq0kbkPQtFrvuVYWh2rMdtYqyeUBYMDMVlJIKlcC/6pebzZTl/vp\nWz9N7orCgRtVXW6rz4oYh0b02Vqp91wre12387OLVjRxB4Vm0hK9xdz9KPAHwD3AU8AOd3+iXu93\n7Gy6Y9aKBs8NEfUNfY1Q7qZHnX1KOcU3eiZeTLTETcDNpCWSC4C7j7j72e6+yt1vqud7xeFsurgn\nTO6KXKEnzBW5Y0Oe5/P5usfQCK3YPVYaZ6Yas++MvhO6lkt9tUq1WEPN1OWW0qiz6fnaIo4cOVL3\nGBqh1brHSuN1dnbS3d0di8b7dqLkUoVjdbnTs1Y08Gx6vqun6enZwTUvNaKLNB8llyrMnE0/sOcB\nkncmIzmbnq8nTEfH7Aah5qZGdJHmouRSpcHBQV555RW2fmxrJGfT8w15vnTp0obEISJSipJLDRKJ\nRGRn0/O1RRw9ejSSuEREQMmlqZVrixgdHY06PBFpY0ouTU5tESISR0ouEWn1O+tFpL0puURgbGzs\neFuJxiUTkRak5NJgxXfWRzVVrohIvbXM8C/NopJRfkVEmp2SS4PFYVwyEZF6U3JpMI3yKyLtQMml\nwTTKr4i0AzXoN5hG+RWRdqDkEgGN8isirU7JJSK6s15EWpnaXEREJHRKLiIiEjolFxERCZ2Si4iI\nhE7JRUREQqfkIiIioVNyERGR0Cm5iIhI6JRcREQkdEouIiISOiUXEREJnZKLiIiETslFRERCF0ly\nMbP3m9kTZpY3szWz1t1gZhkz22tmFxeVrzazx4J1XzYzC8o7zCwdlP/MzFY09q8REZHZorpyeRy4\nAvhpcaGZnQNcCZwLbAC+ZmaLgtVfBz4EDASPDUH5JuBFd+8H/hvwxbpHLyIiZUWSXNz9KXffW2LV\nZcB2d59292eADHCBmS0D3uju97m7A98BLi/a5o5g+a+Ai2auakREJBpxmyysF7iv6Pf9QdmrwfLs\n8pltJgHc/aiZ/T1wGnCo7tFKLGWzWdLpNOOZcQb6B0ilUnR1dUUdlkhbqVtyMbMfAW8useqT7n5X\nvd63HDPbDGwG6OnpYXR0tKbXm5qaqvk16qVdY5uammI8Mw6L4YyzziD7SpZtt29joH+gommk23W/\nhSHO8Sm26tQSW92Si7u/q4rNngP6in5fHpQ9FyzPLi/eZr+ZnQS8CTg8R0y3AbcBrFmzxtetW1dF\niMeNjo5S62vUSzvGls1m6T2zl+ylWVhVtGICum7s4sC+A/MmmHbcb2GJc3yKrTq1xBa3rsg7gSuD\nHmArKTTc3+/uB4GXzWxt0J5yFXBX0TZXB8vvA34ctMtIm0mn0+T78q9PLACrIN+XJ51ORxKXSDuK\npM3FzN4DfAU4Hfi+mT3s7he7+xNmtgN4EjgKXOPurwWbfQT4NnAKsCt4ANwO/JmZZYAjFHqbSRsa\nz4yT686VXJc7LUdmItPgiETaVyTJxd2/B3xvjnU3ATeVKN8DnFei/P8B7w87Rmk+A/0DJHclyXFi\ngkkeTtK/qj+CqETaU9yqxUSqlkqlSEwmYGLWiglITCZIpVKRxCXSjuLWFVmkal1dXYzsHGFo4xD5\nvjy503IkDydJTCYY2TlSUW8xEQmHkou0lMHBQQ7sO0A6nSYzkaF/VT+pVEqJRaTBlFyk5XR2drJp\n06aowxBpa2pzERGR0Cm5iIhI6JRcREQkdEouIiISOjXoi7QRjRgtjaLkItImxsbGjt8D1J0juSvJ\nluu2MLJzhMHBwajDkxaj5CLSBrLZLEMbh143YnSOHEzA0MahikaMFlkItbmItAGNGC2NpuQi0gY0\nYrQ0mpKLSBsY6B8geShZcp1GjJZ6UHIRaQMaMVoaTQ36Im1AI0ZLoym5iLQJjRgtjaTkItJGNGK0\nNIraXEREJHRKLiIiEjolFxERCZ2Si4iIhM7cPeoYImFm/xd4tsaX6QYOhRBOPSi26ii26sU5PsVW\nnVKxnenup8+3YdsmlzCY2R53XxN1HKUotuooturFOT7FVp1aYlO1mIiIhE7JRUREQqfkUpvbog6g\nDMVWHcVWvTjHp9iqU3VsanMREZHQ6cpFRERCp+RSBTP7kpk9bWaPmtn3zOzUonU3mFnGzPaa2cUR\nxPZ+M3vCzPJmtqaofIWZ/YOZPRw8/iQusQXrIt1vs2L5jJk9V7SvhqKMJ4hpQ7BvMmY2HHU8xczs\nF2b2WLCv9kQcy7fM7AUze7yobKmZ/dDMxoOfS2IUWyyONTPrM7PdZvZk8Bn9eFBe/b5zdz0W+AB+\nBzgpWP4i8MVg+RzgEaADWElh9oxFDY7tnwBvBUaBNUXlK4DHI95vc8UW+X6bFedngE9EfZwVxbMo\n2CdnAYuDfXVO1HEVxfcLoDvqOIJYLgTeUXysA7cAw8Hy8MznNSaxxeJYA5YB7wiWu4C/Cz6XVe87\nXblUwd3/xt2PBr/eBywPli8Dtrv7tLs/A2SACxoc21PuvreR71mpMrFFvt9i7gIg4+4/d/dXgO0U\n9pnM4u4/BY7MKr4MuCNYvgO4vKFBBeaILRbc/aC7PxQsZ4GngF5q2HdKLrX7t8CuYLkXmCxatz8o\ni4uVwaX3T8zsnVEHUySO++2jQbXnt6KqRikSx/1TzIEfmdmDZrY56mBK6HH3g8Hy80BPlMGUEKdj\nDTNbAbwd+Bk17DvN5zIHM/sR8OYSqz7p7ncFz/kkcBT4btxiK+Eg8BZ3P2xmq4H/YWbnuvvLMYit\n4crFCXwd+ByFL83PAf+VwkmElDbo7s+Z2RnAD83s6eAsPXbc3c0sTl1kY3WsmVkn8NfAte7+spkd\nW7fQfafkMgd3f1e59Wb2+8ClwEUeVEgCzwF9RU9bHpQ1NLY5tpkGpoPlB81sAjgbCLUBtprYaNB+\nK1ZpnGb2TeDuesZSgYbvn4Vw9+eCny+Y2fcoVOPFKbn80syWuftBM1sGvBB1QDPc/Zczy1Efa2b2\nBgqJ5bvufmdQXPW+U7VYFcxsA3AdsNHdf1W0aidwpZl1mNlKYAC4P4oYZzOz081sUbB8FoXYfh5t\nVMfEar8FH6IZ7wEen+u5DfIAMGBmK81sMXAlhX0WOTNLmlnXzDKFzi5R76/ZdgJXB8tXA3G6go7F\nsWaFS5Tbgafc/daiVdXvu6h7KTTjg0KD8yTwcPD4k6J1n6TQs2cvcEkEsb2HQp38NPBL4J6g/L3A\nE0G8DwHvjktscdhvs+L8M+Ax4NHgw7UsBsfcEIUePBMUqhgjjacorrMo9F57JDi+Io0N+EsKVcCv\nBsfaJuA04F5gHPgRsDRGscXiWAMGKVTNPVr0vTZUy77THfoiIhI6VYuJiEjolFxERCR0Si4iIhI6\nJRcREQmdkouIiIROyUWkBmb2WtGItg8HQ2cs9DVONbOPhBzXlmCE20fN7F4zOzPM1xeZj7oii9TA\nzKbcvbPG11gB3O3u5y1wu0Xu/toc69YDP3P3X5nZh4F17p6qJU6RhdCVi0jIzGyRFeb8eSC4cvj3\nQXlncBXxUDD/yczIxjcDq4Irny+Z2Tozu7vo9b4aDDc0M3fKF83sIeD9ZrbKzH4QDBr5v8zs1wDc\nfbcfHz2ieORukYbQ2GIitTnFzB4Olp9x9/dQuPP67939n5lZB/C3ZvY3FEZ1eI8XBgTsBu4zs50U\n5sk4z91/HcDM1s3znofd/R3Bc+8F/oO7j5vZbwBfA3571vM3cXzkbpGGUHIRqc0/zCSFIr8DvM3M\n3hf8/iYK46XtBz5vZhcCeQrD5lcz/Hsajo1g+8+B/140em1H8RPN7F8Da4DfquJ9RKqm5CISPgM+\n6u73vK6wULV1OrDa3V81s18AJ5fY/iivr7Ke/Zxc8DMBvFQiuc2837sojNn2W14YFVukYdTmIhK+\ne4APB0OYY2ZnByMGvwl4IUgs64GZHlxZClPLzngWOCcYJfpU4KJSb+KFuXieMbP3B+9jZnZ+sPx2\n4BsURu6OzRDz0j6UXETCtw14EnjIzB6n8CV/EoVJ5daY2WPAVcDTAO5+mEK7zONm9iV3nwR2UBh+\nfQfwf8q81+8Cm8xsZlTimU4CXwI6KVSZPRy07Yg0jLoii4hI6HTlIiIioVNyERGR0Cm5iIhI6JRc\nREQkdEouIiISOiUXEREJnZKLiIiETslFRERC9/8BB4h5MOO2/wcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998d9ed68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ny2OqKla3YwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998e70f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2299898d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998b87668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998929198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df.columns:\n",
    "    df.plot.scatter(i,'y', edgecolors=(0,0,0),s=50,c='g',grid=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "linear_model = LinearRegression(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_linear=df.drop('y',axis=1)\n",
    "y_linear=df['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_model.fit(X_linear,y_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_linear = linear_model.predict(X_linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R-square of simple linear fit is very bad, coefficients have no meaning i.e. we did not 'learn' the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "RMSE_linear = np.sqrt(np.sum(np.square(y_pred_linear-y_linear)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root-mean-square error of linear model: 4838.87696595\n"
     ]
    }
   ],
   "source": [
    "print(\"Root-mean-square error of linear model:\",RMSE_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Linear model coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature1</th>\n",
       "      <td>9.172156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>-0.945568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3</th>\n",
       "      <td>10.948377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4</th>\n",
       "      <td>45.069370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5</th>\n",
       "      <td>52.445902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Linear model coefficients\n",
       "Feature1                   9.172156\n",
       "Feature2                  -0.945568\n",
       "Feature3                  10.948377\n",
       "Feature4                  45.069370\n",
       "Feature5                  52.445902"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff_linear = pd.DataFrame(linear_model.coef_,index=df.drop('y',axis=1).columns, columns=['Linear model coefficients'])\n",
    "coeff_linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 value of linear model: 0.347548929728\n"
     ]
    }
   ],
   "source": [
    "print (\"R2 value of linear model:\",linear_model.score(X_linear,y_linear))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x229989a3d68>]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAAHsCAYAAABi/0NiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xt8XFW9///XCm3aJEMpkPSaTgKlSImKnLYavGCJcCgI\nBKktCSDIz1MuyfEo4JeheqocQY0BDwgk3BUVSNraYgpYFJoTUDSSgheYapFgummhbSJCmCZp2mb9\n/pjJkDSTZKaZzMxO3s/Ho482e60kH9y2ec+atT7bWGsREREREZHUl5bsAkREREREJDoK7yIiIiIi\nLqHwLiIiIiLiEgrvIiIiIiIuofAuIiIiIuISCu8iIiIiIi6h8C4iIiIi4hIK7yIiIiIiLqHwLiIi\nIiLiEhOSXUAqy87Otvn5+ckuQ6K0Z88esrKykl2GjIDuofvpHrqf7uHYoPvoPi+++GKbtTZnuHkK\n70PIz89n8+bNyS5DotTQ0MDixYuTXYaMgO6h++keup/u4dig++g+xpht0czTthkREREREZdQeBcR\nERERcQmFdxERERERl1B4FxERERFxCYV3ERERERGXUHgXEREREXEJhXcREREREZdQeBcRERERcQmF\ndxERERERl1B4FxERERFxCYV3ERERERGXUHgXEREREXEJhXcREREREZdQeBcREREZBY7j4PP5yMvL\nIysri7y8PHw+H47jJLs0cTGFdxEREZE4q6+vp6CggMrKShzHoaOjA8dxqKyspKCggPr6+mSXKC41\nIdkFiIiIiIwljuNQXFxMIBAgY+4iphQuJ31aPt27W2hvXEOguYni4mL8fj9erzfZ5YrLaOVdRERE\nJI6qqqrCwT1n6Som584nLT2DybnzyVm6ioy5iwgEAlRXVye7VHEhhXcRERGROKqtrQVgSuFyjOkf\ntYxJY0rhMgBqamoSXpu4n8K7iIiISBy1tbUBkD4tP+J4ek5+v3kisVB4FxEREYmj7OxsALp3t0Qc\n725t6TdPJBYK7yIiIiJxVFJSAkB74xqs7ek3Zm0P7Y1rASgtLU14beJ+Cu8iIiIicVReXo7H46Gz\nuYnWdTfRtX0LPXs76Nq+hdZ1N9HZ3ITH46GsrCzZpYoLqVWkiIiISBx5vV7q6uqC7SKbm+hsbuo3\n7vF4qKurU5tIOSRaeRcRERGJs6KiIvx+Pz6fD6/XS2ZmJl6vF5/Ph9/vp6ioKNkliktp5V1ERERk\nFHi9XioqKqioqEh2KTKGaOVdRERERMQlFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETE\nJRTeRURERERcQuFdRERERMQlFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURE\nRERcQuFdRERERMQlFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURERERcQuFd\nRERERMQlFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETGLcdx8Pl85OXlkZWVRV5eHj6f\nD8dxkl1aRArvIiIiIjIu1dfXU1BQQGVlJY7j0NHRgeM4VFZWUlBQQH19fbJLHGBCsgsQEREREUk0\nx3EoLi4mEAiQMXcRUwqXkz4tn+7dLbQ3riHQ3ERxcTF+vx+v15vscsO08i4iIiIi405VVVU4uOcs\nXcXk3PmkpWcwOXc+OUtXkTF3EYFAgOrq6mSX2o/Cu4iIiIiMO7W1tQBMKVyOMf0jsTFpTClcBkBN\nTU3CaxuKwruIiIiIjDttbW0ApE/LjzienpPfb16qUHgXERERkXEnOzsbgO7dLRHHu1tb+s1LFQrv\nIiIiIjLulJSUANDeuAZre/qNWdtDe+NaAEpLSxNe21AU3kVERERk3CkvL8fj8dDZ3ETrupvo2r6F\nnr0ddG3fQuu6m+hsbsLj8VBWVpbsUvtRq0gRERERGXe8Xi91dXXBdpHNTXQ2N/Ub93g81NXVpVSb\nSNDKu4iIiIiMU0VFRfj9fnw+H16vl8zMTLxeLz6fD7/fT1FRUbJLHCClV96NMZOB54BJBGv9ubX2\nW8aYo4DVQD7QAiy31v4r9DkrgS8BB4D/stb+KnR9AfAQkAH8EviKtdYm8r9HRERERFKL1+uloqKC\nioqKZJcSlVRfed8LFFlrTwI+AiwxxhQCNwCbrLXzgE2hjzHGnAiUAAXAEqDaGHNY6GvdDawA5oV+\nLUnkf4iIiIiIyEildHi3QYHQhxNDvyxQDPwkdP0nwPmhPxcDtdbavdbafwCvAR81xswEplhrG0Or\n7T/t8zkiIiIiIq6Q0ttmAEIr5y8CxwFV1to/GGOmW2vfCk3ZCUwP/Xk20Njn07eHru0L/fng65G+\n3xXAFQDTp0+noaEhTv8lMtoCgYDul8vpHrqf7qH76R6ODbqPY1fKh3dr7QHgI8aYqcBjxpgPHjRu\njTFx27turb0PuA9g4cKFdvHixfH60jLKGhoa0P1yN91D99M9dD/dw7FB93HsSultM31Za98B/o/g\nXvVdoa0whH7fHZq2A5jT59NyQ9d2hP588HUREREREddI6fBujMkJrbhjjMkAzgD+BmwALgtNuwyo\nC/15A1BijJlkjDmG4MHUF0JbbNqNMYXGGANc2udzRERERERcIdW3zcwEfhLa954GrLHWPmGM+T2w\nxhjzJWAbsBzAWus3xqwBtgD7gfLQthuAMt5vFbkx9EtERERExDVSOrxba/8CnBzh+j+BzwzyOd8B\nvhPh+mbggwM/Q0RERETEHVJ624yIiIiIiLxP4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURE\nRERcQuFdRERERMQlFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURERERcQuFd\nRERERMQlFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURERERcQuFdRERERMQl\nFN5FRERERFxC4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURERERcQuFdRERERMQlFN5FRERE\nRFxC4V1ERERExCUU3kVEREREXELhXURERETEJRTeRURERERcQuFdRERERMQlFN5FRERERFxC4V1E\nRERExCUU3kVEREREXELhXURERETEJRTeRURERERcQuFdRERERMQlFN5FRERERFxC4V1ERERExCUU\n3kVEREREXELhXURERETEJRTeRURERERcQuFdRERERMQlFN5FRERERFxC4V1ERERExCUU3kVERERE\nXELhXURERETGrc7OTiorKzHG8LGPfYz29vZklzSkCckuQEREREQkkbq6urj//vt58cUXWb9+Pe+9\n9x4AL7zwAh0dHUyZMiXJFQ5O4V1ERERExjxrLY2NjTz66KPcdddd/cYWLVpEZmYmt912GzNmzEhS\nhdFReBcRERGRMWv16tWUlJREHLv88stZuXIl8+bNS3BVh0573kVEZFxwHAefz0deXh5ZWVnk5eXh\n8/lwHCfZpYlInLW0tFBRUYExpl9wnzVrFtdddx0vvPACPT09/OhHP3JVcAetvIuIyDhQX19PcXEx\ngUAgfM1xHCorK6murqauro6ioqIkVigiI9Xa2srnPvc5nn/++YjjN998MzfccAOHHXZYgiuLL4V3\nEREZ0xzHCQf3jLmLmFK4nPRp+XTvbqG9cQ2B5iaKi4vx+/14vd5klysiMXjrrbeoq6tjw4YN/PrX\nv+bAgQPhsZKSEi666CLOPPNM0tPTk1hlfCm8i4jImFZVVRUO7jlLV2FMcMfo5Nz5TFq6itZ1NxFo\nbqK6upqKiookVysiw9m7dy93330311xzTb/rEyZMYN68ecybN4+HHnqInJycJFU4urTnXURExrTa\n2loAphQuDwf3XsakMaVwGQA1NTUJr01EorNv3z4efPBBVqxYwYwZMwYE97vvvpu33nqLV199lSef\nfHLMBnfQyruIiIxxbW1tAKRPy484np6T32+eiKQGay0vvfQSjzzyCLfddlu/sZNOOokJEyZw++23\n88lPfjJJFSaHwruIiIxp2dnZOI5D9+4WJufOHzDe3doSniciyffEE09w7rnnRhy75JJLWLlyJSee\neGKCq0od2jYjIiJjWm+buPbGNVjb02/M2h7aG9cCUFpamvDaRCRox44d/O///i/GmH7Bfdq0afzX\nf/0Xv/3tbzlw4AA/+9nPxnVwB628i4jIGFdeXk51dTWB5iZa193ElMJlpOfk093aQnvjWjqbm/B4\nPJSVlSW7VJFx5e233+bCCy/kmWeewRiDtbbf+De+8Q1uvPFGJkxQXO1L/2uIiMiY5vV6qaurC7aL\nbG6is7mp37jH46Gurk5tIkUSoK2tjQ0bNlBXV8fGjRvZt28fENzffsEFF3DRRRdx9tlnk5GRkeRK\nU5fCu4iIjHlFRUX4/X6qq6upqamhra2N7OxsSktLKSsrU3AXGUX79u3j/vvvp7y8vN/1tLQ0cnNz\nmTt3Lo8++iizZs1KUoXuovAuIiLjgtfrpaKiQr3cRRLgwIEDrF69mt/+9resWbOGf/7zn/3G77jj\nDpYtW8aMGTOSVKF7KbyLiIiIyIhZa/nLX/5CTU0N3//+9/uNzZ8/H2MMP/zhDzn99NOTVOHYoPAu\nIiIiIofsmWee4bzzzqOzs3PA2PLly/n617/Ohz/8YYwxSahu7FGryHHAcRx8Ph95eXlkZWWRl5eH\nz+fDcZxklyYiIuOUfja5265du7jzzjuZOHEiZ5xxRji4H3300Vx99dVs2rSJ/fv3s3r1ak466SQF\n9zjSyvsYV19fH+ywEAiErzmOQ2VlJdXV1dTV1VFUVJTECkVEZLzRzyZ3am9v55JLLuHxxx8nLS2N\nnp7+z0247rrr+N73vsfEiROTVOH4oPA+hjmOE/7HMWPuIqYULid9Wj7du1tob1xDoLmJ4uJi/H6/\nOi2IiEhC6GeTu7zzzjs8+eSTPPbYYzzxxBPs3bsXgJ6eHs4991wuuugizjnnHDweT5IrHT+0bWYM\nq6qqCv/jmLN0FZNz55OWnsHk3PnkLF1FxtxFBAIBqqurk12qiIiME/rZlPr279/PAw88gDGGI488\nkksuuYR169bR3d3N0UcfzYIFC9i2bRsbNmygpKREwT3BFN7HsNraWgCmFC7HmP632pg0phQuA6Cm\npibhtYmIyPikn02pqaenh/Xr1/OVr3yF3NxcVqxY0W/81ltvxXEc2tra2Lx5s94VSSJtmxnD2tra\nAEiflh9xPD0nv988ERGR0aafTanlr3/9K48++ig333xzv+vHHXcc3d3d3HHHHRQXFyepOolE4X0M\ny87OxnEcune3MDl3/oDx7taW8DwREZFE0M+m5Pvd737H+eefT1tbG9bafmOf+9znWLlyJQsXLlSH\nmBSlbTNjWElJCQDtjWuwtv+JcGt7aG9cC0BpaWnCaxMRkfFJP5uSo62tjXvuuYfMzEw+8YlP0Nra\nirWWI444gi996Uts3LiRvXv3sn79ehYtWqTgnsJSOrwbY+YYY/7PGLPFGOM3xnwldP0oY8zTxpi/\nh34/ss/nrDTGvGaM2WqMObPP9QXGmJdDY3eYcfD/yvLycjweD53NTbSuu4mu7Vvo2dtB1/YttK67\nic7mJjweD2VlZckuVURExgn9bEqcQCDAhRdeiDGGmTNncvXVV/d7kNJVV13Frl27eOCBB1iyZAnp\n6elJrFailerbZvYD11lrXzLGHA68aIx5GvgisMlaW2GMuQG4AfAZY04ESoACYBbwjDHmeGvtAeBu\nYAXwB+CXwBJgY8L/ixLI6/VSV1cXbMnV3ERnc1O/cY/HQ11dnQ6diIhIwuhn0+jas2cPTz31FNXV\n1TQ2NtLR0QEEO8gsWbIk3NrxyCOPHOYrSapK6fBurX0LeCv05/eMMX8FZgPFwOLQtJ8ADYAvdL3W\nWrsX+Icx5jXgo8aYFmCKtbYRwBjzU+B8xnh4BygqKsLv91NdXU1NTQ1tbW1kZ2dTWlpKWVmZ/nEU\nEZGE08+m+Orp6eGRRx7h0ksvHTDm8XiYM2cOjz/+OHPnzk1CdRJv5uCDCoNONCYfOBF41lq7J3Rt\nArCKYBDeA9xirX1sVAoNfv/ngA8CjrV2aui6Af5lrZ1qjLkLaLTWPhwae5BgQG8BKqy1p4eufwrw\nWWvPifB9rgCuAJg+ffqC3pZWkvoCgYB6zbqc7qH76R66n+6hO1hraWpq4qWXXmLTpk0DuvNceuml\nnHXWWcyYMSNJFUqsTjvttBettQuHmxfLyvu3gPOA6X2u/TfB8N5rjTHmU70r3PFijPEA64CvWmvb\n+25Xt9ZaY0x0r0CiYK29D7gPYOHChXbx4sXx+tIyyhoaGtD9cjfdQ/fTPXQ/3cPU9tprr1FTU8M3\nv/nNftfz8vIIBALceeedlJaW6j6OYbGE91MI7jPfD2CCT1YoA/4G/DswA3gGuAa4MF4FGmMmEgzu\nj1hr14cu7zLGzLTWvmWMmQnsDl3fAczp8+m5oWs7Qn8++LqIiIhISnvppZe44IILaG1tDe9h73XO\nOeewcuVKTjnlFHWIGSdi6TYzHdjW5+OPANlAlbV2u7V2M1AHLIpXcaEtMQ8Cf7XW/m+foQ3AZaE/\nXxb6vr3XS4wxk4wxxwDzgBdCe+fbjTGFoa95aZ/PEREREUkp77zzDg8++CBHHHEECxYsYNu2bXR0\ndODxeLj00kupq6ujs7OTxx9/nI9//OMK7uNILCvvE4G+21M+Efq4vs+17cDMONTV93t8AXjZGPOn\n0LWvAxUEt+h8ieALiuUA1lq/MWYNsIVgp5ryUKcZCL5L8BCQQXAf/Jg/rCoiIiLu0dnZSVlZGQ89\n9BDp6el0d3f3G//iF79IVVUVmZmZSapQUkEs4X078OE+H58NtFlr/9rn2jSgPR6FAVhrfwsM9lLy\nM4N8zneA70S4vpngYVcRERGRlNDV1cXTTz/Nz3/+cx577DHee+89ALq7uykqKuKiiy7i3HPPZdq0\naUmuVFJFLOH9CeAaY8ytQBdwBvDjg+YcT/+tNSIiIiLSh7WWtWvXcuGFA48ITpgwgdmzZ/PUU09x\nwgknJKE6SXWxhPdKgi0hrw19vINgBxoAjDHTCB5qvSNu1YmIiIiMEc899xxPPfUUNTU1tLS09Bv7\nn//5H0pLS5k3b15yihPXiDq8W2t3G2M+xPvbVZ611r7XZ0o28P+AX8WxPhERERHX+ulPf8pll102\n4Prs2bN5++23ueuuu7j88st14FSiFtMTVq21nQS3z0Qa20LwoKiIiIjIuPWb3/yGU089NeLYmWee\nycqVK/nUpz5FWlosTf9EgmIK772MMScA8wGPtfZn8S1JRERExF3efPNNvvjFL/L0009HHD/22GP5\n85//rKfXyojFFN6NMR8BHgBO7nP5Z6GxTxNsv3ihtfbxuFUoIiIikoLa2trIyckZcs6OHTuYNWtW\ngiqS8SDq92uMMccDDcAHgB8ysE/6c8DbwOfjVZyIiIhIKunq6uLCCy/EGBMxuJ900kls3boVay3W\nWgV3ibtYNlt9C0gHPmatvRZo6jtorbXA74njE1ZFREREks1ay3333YcxhoyMDNasWTNgzt133421\nlj/96U8cf/zxSahSxotYwvtngPWhg6mDeQPQS0wRERFxvVWrVmGMIS0tjSuvvHLA+Le//e3wCvtV\nV12VhAplPIplz/uRBJ+yOhRDcHVeRERExHXWr1/P0qVLBx2/8sorqa6uVqcYSZpYwvsu4Lhh5hQQ\nXH0XERERcYUXX3yRhQsXDjp+1VVXcfvttzNp0qQEViUSWSzhvR4oNcZ8wFq79eBBY8wigltrquJV\nnIiIiMhoaG1tZcWKFdTV1Q065x//+Af5+fmJK0okCrG85/M9YD/wnDHmakJ7240xBaGPHwfeA26N\ne5UikrIcx8Hn85GXl0dWVhZ5eXn4fD4cx0l2aSIi/bS3t2OMwRjDtGnTIgb35ubm8D52BXdJRVGH\n99Bq+1KCe9rvAv6D4B73vxBcbU8HLrDW6ie2yDhRX19PQUEBlZWVOI5DR0cHjuNQWVlJQUEB9fX1\nyS5RRMa5/fv3s2LFCowxHHHEEQPGjzvuOP785z+HA/uxxx6bhCpFohfTQ5qstU8ZY44BLgMKgaOB\nd4FG4MfW2rfjX6KIpCLHcSguLiYQCJAxdxFTCpeTPi2f7t0ttDeuIdDcRHFxMX6/H6/Xm+xyRWQc\nsdby6KOPcskllww65/vf/z7XX399AqsSiY+Yj0pba9+x1v7QWltqrf13a+0ya+0PFNxFxpeqqqpw\ncM9ZuorJufNJS89gcu58cpauImPuIgKBANXV1ckuVUTGidtvvz3c2jFScL/uuuvo6enBWqvgLq6l\nPkcickhqa2sBmFK4HGP6/1NiTBpTCpcBUFNTk/DaRGT8+PWvfx3ex37NNdcMGC8pKaG7uxtrLbfe\neivGmCRUKRI/UW+bMcacGu1ca+1zh1aOiLhFW1sbAOnT8iOOp+fk95snIhIvfr+fD37wg4OOX3rp\npdx9991kZmYmsCqRxIhlz3sDYKOce1jspYiIm2RnZ+M4Dt27W5icO3/AeHdrS3ieiMhIvfPOO5SX\nl/Poo48OOmfLli3Mnz/w3yORsSSW8P5tIof3qcAi4OME20W+FIe6RCTFlZSUUFlZSXvjGiYtXdVv\n64y1PbQ3rgWgtLQ0WSWKiMt1dHSQlZU15By/38+JJ56YoIpEki/q8G6tvXGocWPMF4E7gW+MrCQR\ncYPy8nKqq6sJNDfRuu4mphQuIz0nn+7WFtob19LZ3ITH46GsrCzZpYqIi/T09PC1r32N2267LeL4\nrFmzeOyxx/joRz+a4MpEUkNMrSKHYq19yBhzMfBd4Lx4fV0RSU1er5e6urpgu8jmJjqbm/qNezwe\n6urq1CZSRKKyfv16li5dOuj4ypUr+e53v5vAikRSU7y7zfwJiPpgq4i4W1FREX6/H5/Ph9frJTMz\nE6/Xi8/nw+/3U1RUlOwSRSSF/fjHPw53iokU3L/0pS+FWzsquIsExW3lPWTOKHxNEUlhXq+XiooK\nKioqkl2KiLjA7373Oz7xiU8MOn7WWWexfv16Jk+enMCqRNwjLkHbGHMYcDnweeC38fiaIiIiMja8\n/vrrzJ07d9Dxz3/+8zz44INMmTIlgVWJuFMsfd5fH+JrTA/93g18PQ51iYiIiIsFAgGuvfZa7r//\n/kHnNDU1sXDhwgRWJeJ+say8pxG5VeQ+4GXgBeBOa+1f41GYiIiIuEt3dzeHH3443d3dg87ZvHkz\nCxYsSGBVImNLLK0i80exDhEREXEhay033ngj3/72tyOOH3HEEWzYsIFTT1U/C5F40OFSERERidmv\nfvUrlixZMuh4WVkZVVVVCaxIZHxQeBcREZGoDNeLfenSpaxevZrDDjssgVWJjC+DhndjzDcP8Wta\na+1Nh/i5IiIikkL++Mc/8m//9m+DjhcWFvL000/j8XgSWJXI+DXUyvuNh/g1LaDwLiIi4lI7duwg\nNzd30PGzzz6bn/3sZxx11FEJrEpEYOjwflrCqhAREZGk6urqYuXKldx+++2DzmloaODTn/50AqsS\nkYMNGt6ttc8mshARERFJrAMHDpCXl8eOHTsGnfPss8+qU4xICklLdgEiIiKSWD/4wQ8wxjBhwoQB\nwf2www7jqaeewlqLtVbBXSTFKLyLiIiMA8899xzGGIwxfO1rXxswXlpaSk9PD8888wxnnnlmEioU\nkWjE1CrSGDMT+G/gTGA2kB5hmrXWqgWliIhIkj3zzDOcccYZg45/5jOf4Ze//CXp6ZF+nItIKoo6\nZBtjZgMvANMBPzAJ2AbsBY4Nfa0/Ae/Gv0wRERGJxtatWznhhBMGHZ8/fz7PP/88Rx55ZAKrEpF4\niWXbzDeBGcASa+1JoWs/ttaeQDC8/wrIAC6Ib4kiIiIylNbWVqZOnYoxJmJwP/XUU9m5cyfWWrZs\n2aLgLuJisYT3M4GnrLXPHDxgrd0OLCMY3v8nTrWJiIjIIPbt28c3vvENjDFMmzaNd98d+Mb3hg0b\nsNby7LPPMn369CRUKSLxFsve9BnAmj4fHyAY1gGw1gaMMU8DxcB/xac8ERER6WWt5SMf+Qh/+ctf\nBp3z5JNPcvbZZyewKhFJpFhW3tvpf0D1XwQPrfb1LpAz0qJERETkfffccw/GGNLS0iIG98ceeyzc\n2lHBXWRsiyW8bwPm9Pn4z0CRMSYTwBiTBvw7sD1+5YlIIjiOg8/nIy8vj6ysLPLy8vD5fDiOk+zS\nRMatF154Idza8eqrrx4wfvbZZ3PgwAGstZx//vlJqFBEkiGW8L4JOM0YMzH08U+AWcDvjDG3AM8D\nBcDq+JYoIqOpvr6egoICKisrcRyHjo4OHMehsrKSgoIC6uvrk12iyLjR2NjIxIkTMcbwsY99bMD4\nggUL6OjowFrLk08+SVqaHtciMt7Esuf9QYJbZbKBt6y1DxtjFgBfBj4cmlMLfCe+JYrIaHEch+Li\nYgKBABlzFzGlcDnp0/Lp3t1Ce+MaAs1NFBcX4/f78Xq9yS5XZEzatm0b+fn5g47PnDmTP/7xjzpw\nKiJADCvv1tq/W2u/b619q8+1a4CZwCnATGvtRdbarlGoU0RGQVVVVTi45yxdxeTc+aSlZzA5dz45\nS1eRMXcRgUCA6urqZJcqMqa8++67HHPMMRhjIgb3hQsX4jgO1lrefPNNBXcRCRvx+23W2lZr7R+s\ntbviUZCIJE5tbS0AUwqXEzy28j5j0phSuAyAmpqahNcmMtYcOHCA7373uxhjmDp1Ki0tLQPm/Oxn\nP8NaS1NTE3PmzBn4RURk3IvlCatrgB8Dv7LW9oxeSSKSKG1tbQCkT8uPOJ6ek99vnojExlrLGWec\nwaZNmwads3r1apYvX57AqkTEzWJZef888ASwwxhzizHmg6NUk4gkSHZ2NgDdu1sijne3tvSbJyLR\nefjhh8OtHSMF90ceeYSenh6stQruIhKTWMJ7IXAvwV7v1wF/NsZsNsZ82Rijn+wiLlRSUgJAe+Ma\nDn5DzdpZAub1AAAgAElEQVQe2hvXAlBaWprw2kTc5i9/+Uu4teMXvvCFAeOFhYXs27cPay0XXXQR\nxpgkVCkibhfLgdUXrLVlBA+oLgd+SbDLzA8JrsavN8acb4yJpYONiCRReXk5Ho+HzuYmWtfdRNf2\nLfTs7aBr+xZa191EZ3MTHo+HsrKyZJcqkpJefvlljj76aIwxnHTSSQPGjz32WN59912stfz+979n\nwgT9iBSRkYn5XxFrbTfwc+Dnxpgc4BLgMuB8oBj4JzAtnkWKyOjwer3U1dUF20U2N9HZ3NRv3OPx\nUFdXpzaRIn3s3LmTvLw8uru7I45PmjSJV199VX9vRGRUjKjbTKjTzG3AycDXgP3A0fEoTEQSo6io\nCL/fj8/nw+v1kpmZidfrxefz4ff7KSoqSnaJIknX0dHBySefjDGGmTNnDgju8+fP57XXXsNaS1dX\nl4K7iIyaEb1/Z4z5AMFV90uA2YAB/h6HukQkgbxeLxUVFVRUVCS7FJGU0dPTw5133slXv/rVQefc\neeed/Od//mcCqxKR8S7m8G6MmQqUEgztiwgG9naCT2D9ibX2+bhWKCIikkAXXXTRkM82uP/++/mP\n//iPBFYkIvK+WPq8nwtcCpxDsOOMBZ4BfgKs15NVRUTErR577DEuuOCCQcfvvfdeVqxYoQ4xIpJ0\nsay814V+f5VgYP+ptXZH/EsSEREZfVu3buWEE04YdPyEE07gT3/6E5MmTUpgVSIiQ4slvN9LcFtM\n42gVIyIiMppee+01zjjjDFpaWiKOH3XUUWzdulUPJhORlBV1eLfWXj2ahYiIiIyGN954Y9juL3/7\n29/4wAc+kKCKREQO3SG3ijTGFBtjfhTPYkREROKho6Mj/LTTSMH9mGOOwe/3Y63FWqvgLiKuMZI+\n7x8h2HFGREQk6ay13HvvvRhjyMrKijjnzDPPxFrL66+/zoknnpjgCkVERk7PaRYREVf7wAc+wKuv\nvjro+Ec/+lH+8Ic/JLAiEZHRM6InrIqIiCTDd7/73fC2mEjBPS8vj3379mGtVXAXkTFFK+8iIuIK\nDQ0NnHbaaYOOT58+nebm5kG3zIiIjAUjWXn/E/DTeBUiIiJysO3bt3PyySdjjBk0uL/yyitYa9m5\nc6eCu4iMeYe88m6treP9BzeJiIjExfbt25kzZ86Qc37xi19QXFycoIpERFJH1Cvvxpg7jDHzR7MY\nEREZn/bu3Rvewx4puE+bNo3NmzeHWzsquIvIeBXLtpn/BF4xxjxnjLnYGJM+WkWJiMj4cNZZZ2GM\nYfLkyRHHjz/+eKy17Nq1iwULFiS4OhGR1BPLtpllwJXAZ4BPAD80xjwE3G+t3ToKtYmIyBhkjBl2\nTk9PT1TzRETGm6hX3q2166y1/w4cB1QC3cC1wBZjTL0xZrkxZuIo1SkiIi62fPny8LaYwQQCgfC2\nGAV3EZHIYu42Y639h7V2JeAluBq/Cfg0UANsN8ZUGGPmxqtAY8yPjDG7jTGv9Ll2lDHmaWPM30O/\nH9lnbKUx5jVjzFZjzJl9ri8wxrwcGrvD6CeDpDjHcfD5fOTl5ZGVlUVeXh4+nw/HcZJdmkhUfvGL\nX4QD+9q1ayPO2bFjRziwq1OMiMjwDrlVpLV2f5/V+FOAN4Ec4HpgqzHmCWNMPDYoPgQsOejaDcAm\na+08gi8ebgAwxpwIlAAFoc+pNsYcFvqcu4EVwLzQr4O/pkjKqK+vp6CggMrKShzHoaOjA8dxqKys\npKCggPr6+mSXKBJRa2trOLB/7nOfizjn/vvvDwf2WbNmJbhCERF3G9FDmowxnya4D/5zwCSgFXgE\n+DfgbOBMY8wl1trVh/o9rLXPGWPyD7pcDCwO/fknQAPgC12vtdbuBf5hjHkN+KgxpgWYYq1tDNX9\nU+B8YOOh1iUyWhzHobi4mEAgQMbcRUwpXE76tHy6d7fQ3riGQHMTxcXF+P1+vF5vsssVYefOncyc\nOXPIOVdeeSX33HNPgioSERm7jLU2tk8IblH5InAFcDxggOcJrmyvtdbuC837KLAeeM9aO6IWk6Hw\n/oS19oOhj9+x1k4N/dkA/7LWTjXG3AU0WmsfDo09SDCgtwAV1trTQ9c/BfistedE+F5XhP7bmD59\n+oLa2tqRlC4JFAgE8Hg8yS5jxHbs2MHOnTtJm5TFhCMHBqL9/3qLnr17mDFjBrNnz05ChaNnrNzD\n8eDAgQOcfvrpQ8658sorKSkpSVBFEi/6ezg26D66z2mnnfaitXbhcPOiXnkPBd4rgKXAZCAA3Avc\nba19+eD51toXjDE/JrgiPmqstdYYE9srkKG/3n3AfQALFy60ixcvjteXllHW0NDAWLhfeXl5OI7D\n9ItvYXLuwL+iXdvfY9cj1+P1etm2bVsSKhw9Y+UejmXXXnstt91225BzYl0UktSiv4djg+7j2BXL\ntplnQ7/7Ca6y/9RaGxjmc3aEfsXbLmPMTGvtW8aYmcDuPt+v79M9cvvUkBvhukjKaWtrAyB9Wn7E\n8fSc/H7zREZbNOf79+3bx4QJE2hoaBj9gkRExrFYDqzWAp+21n7IWlsdRXDHWnuPtfaYQy9vUBuA\ny0J/vgyo63O9xBgzyRhzDMGDqS9Ya98C2o0xhaFtNpf2+RyRlJKdnQ1A9+6WiOPdrS395omMhnPO\nOWfY1o67du0KHzydMGFER6hERCRKsfR5v8ha+5vRLCYSY0wN8HvgA8aY7caYLwEVwBnGmL8Dp4c+\nxlrrB9YAW4CngHJr7YHQlyoDHgBeA5rRYVVJUb17hNsb12BtT78xa3tobwy23CstLU14bTK2/fKX\nvwwH9ieffDLinFdffTUc2KdNm5bgCkVEJOWXSqy1gyWUzwwy/zvAdyJc3wx8MI6liYyK8vJyqqur\nCTQ30bruJqYULiM9J5/u1hbaG9fS2dyEx+OhrKws2aXKGPD6668zd+7Qj+b48pe/zB133JGgikRE\nZCgpH95Fxhuv10tdXV2wXWRzE53NTf3GPR4PdXV1ahMph+xf//oXRx111JBz5syZoweCiYikoEN+\nSJOIjJ6ioiL8fj8+nw+v10tmZiZerxefz4ff76eoqCjZJYrLWGvDW2IGC+7Lli0Lb4lRcBcRSU1a\neRdJUV6vl4qKCioqKpJdius4jkNVVRW1tbW0tbWRnZ1NSUkJ5eXl4+4di6ysLDo6Ooac09PTE1VH\nGRERST6tvIvImFJfX09BQQGVlZU4jkNHRweO41BZWUlBQQH19fXJLnHU9a6wG2MGDe7t7e3hVXYF\ndxER91B4F5Exw3Gc4FmBQICMuYuYfvEtzLlmLdMvvoWMuYsIBAIUFxePyS0hX/jCF4Zt7di3U8zh\nhx+ewOpERCReFN5FZMyoqqoKB/ecpauYnDuftPQMJufOJ2fpqnCAr66uTnapcbFx48ZwYH/44Ycj\nznn66afDgX3evHkJrlBEROJt0D3vxphTD/WLWmufO9TPFRE5VLW1tQBMKVyOMf3XJoxJY0rhMjqb\nm6ipqXHtWYI333yT2bNnDznn1FNP5dlnnx1yjoiIuNNQB1YbAHuIX/ewQ/w8EZFD1tbWBkD6tPyI\n4+k5+f3muUVXVxcZGRnDzrP2UP/JFhERtxgqvH+bQw/vIiIJl52djeM4dO9uYXLu/AHj3a0t4Xlu\nEM1BUgV2EZHxZdDwbq29MYF1iIiMWElJCZWVlbQ3rmHS0lX9ts5Y20N741oASksHe3Bz8p144on8\n9a9/HXLO/v37OewwvcEpIjIe6cCqiIwZ5eXleDweOpubaF13E13bt9Czt4Ou7VtoXXcTnc1NeDwe\nysrKkl1qP/Pnzw8fPB0suG/fvj188FTBXURk/NJDmkRkzPB6vdTV1QXbRTY30dnc1G/c4/FQV1eX\nEg9q+u///m++853vDDln06ZNepquiIj0E1N4N8ENmJ8HzgRmA5MiTLPW2s/EoTYRkZgVFRXh9/up\nrq6mpqYm/ITV0tJSysrKkhrc//CHP1BYWDjknNWrV7N8+fIEVSQiIm4TdXg3xkwCfgksBgzBw6x9\nT1PZPtdFRJLG6/VSUVGREu0g3333XaZOnTrknJkzZ/Lmm28mqKLU5zgOVVVV1NbWhl98lZSUUF5e\nnhLvmoiIJFMse959wGnAzUA2waB+IzALuAh4A6gF0uNbooiIu/T09IT3sA8V3Hv3sCu4v6++vp6C\nggIqKytxHIeOjg4cx6GyspKCggLq6+uTXaKISFLFsm1mGfCStfZb8H4LM2vtTqDWGPMC8Cfgq8AP\n4lyniEjKU2vHkXEcJ3heIfSU3CmFy0mflk/37hbaG9cQaG6iuLgYv9+vFXgRGbdiWXmfCzzf52ML\nTAx/YO3rwJPAF+NSmYiIC5x11lnhVfbBdHV1hVfZZXBVVVXh4J6zdBWTc+eTlp7B5Nz55CxdRcbc\nRQQCAaqrq5NdqohI0sQS3vcBXX0+fg/IOWjONuDYkRYlIpLKiouLw4H9qaeeijjnlVdeCQf2SZMi\nne2Xg9XW1gIwpXB5vx79AMakMaVwGQA1NTUJr01EJFXEEt63E+ww0+tV4JSD5pwMvD3SokSG4zgO\nPp+PvLw8srKyyMvLY8eOHTiOk+zSJAYH38eXX34Zn8+Xkvfx3nvvDQf2DRs2RJxTW1sbDuwFBQUJ\nrtD92traAEiflh9xPD0nv988EZHxKJbw/jzw8T4f/wL4kDHmAWPMZ40xtwCnAw1xrE9kgMEOtO3c\nuVMH2lJQpBdaPp+PmpqaAfexu7s7pQ4mbt26NRzYr7rqqohz7rrrrnBgv/DCCxNc4diSnZ0NQPfu\nlojj3a0t/eaJiIxHsRxYfRSYY4zJt9a2ALcDxcD/B1xOsPvMa8AN8S5SpNdQB9rSJmURCAR0oC2F\n1NfXh+9Xr97OIb363seJRx0I7mtO4sHErq4uMjIyhp2n/evxV1JSQmVlJe2Na5i0dFW/rTPW9tDe\nuBaA0tLSZJUoIpJ0Ua+8W2sbrLVnhYI71toO4BMEu9B8HSgFPmKt3TEahYrA0AfaJhw5UwfaUsjB\nL7SmX3wLc65Zy/SLb2HC1BkAA+6jSZ+ctIOJvSvsQwX33hV2BffRUV5ejsfjobO5idZ1N9G1fQs9\nezvo2r6F1nU30dnchMfjoaysLNmliogkTSzbZgaw1u631q6z1n7fWrs6FOhFRs1QB9qC13WgLVUM\n9ULL9hwAkn8wsTewD9UppqenR4E9QbxeL3V1deEAv+uR63nj9uXseuT6cHCvq6vTu2oiMq6NKLyL\nJJoOtLnHUC+0ejrbgeTcx9zc3GED+zvvvBMO7NH0bpf4KSoqwu/34/P58Hq9ZGZm4vV68fl8+P1+\nioqKkl2iiEhSRb3n3RhzabRzrbU/PbRyRIaWnZ2N4zh0725hcu78AeM60JY6hnqhlZYxhQP7WhN2\nH88666xBWzr21buye8QRR8Tl+8qh8Xq9VFRUUFFRkexSRERSTiwr7w8BPx7mV+8ckVFRUlICQHvj\nGqztGTCuA22xG6wbzEjbNQ7VOSRr/qlA5PsYr4OJGzZsGLYXe8bxHw/vw+/dZ19cXJySrSpFREQg\ntvB+OcHOMgf/uhaoIfjE1Z+HromMiqEOtO3/11tRH2gbrcDqNoO13YxHu8ahXmh5Tj4bTNqA+2i7\nu0Z0MNFxnHBgLy4uHnRextxFeK/fwLTPfV1P8BQREVeJetuMtfYnQ40bY34MPAncMdKiRAbTe6Ct\nuLiYQHMTnc1N4bGek2+N6kDbUO0Lq6urqaurGxf7aodqu9neuGbE7RrLy8uprq4mEAroUwqXkZ6T\nT3drS3BlPRToO/vcx3233hrzwcT9+/czceLEYedZa8nLy8NxnCEPynY2N1FTU6MtGyIikpJi6fM+\nJGvtJmPMU8C3gbGffCRpeg+0VVdXU1NTQ1tbG9nZ2cyYMWPYoDnagdVNDu4G0xtmJ+fOZ9LSVbSu\nu4lAcxPV1dWHFGSHeqEFwf3l9913H3/+85/D9zE9PR2fz0dZWdmw//tHc5D04A4xOvAsIiJuF+9u\nM68CC+P8NUUG6D3Qtm3bNvbs2cO2bduYPXv2sIFvqPaF423bxFDdYOLVrnG4ziGlpaX97uOHPvQh\nKioqBr2P0bR27O7uHrS1o57gKSIibhfv8H4iwb3vIikpEYHVLRK1Ch3phdZQAf1gK1asGDawt7S0\nhAP7UFtohtqHP9af4KlzHiIiY8OIw7sxJs0Yk2eMuRk4C/jNyMsSGR3aNvG+VF6FXrlyZTiwP/DA\nAxHn1NbWhgN7Xl5eVF93vD7BczQPJouISGLF0ue9h6FX1Q3wT+D/jbQokdGiPvHvKykpobKykvbG\nNUzqs+cdkrMK3djYyGmnnTbknAsuuIB169Yd8veIZh/+WHuCp1vOeTiOQ1VVFbW1teFzLCUlJZSX\nl4+p+yEiMlKxrLw/N8ivBuAx4AbgRGvtX+Nco0jcjOdtEwdLhVXod999N7zCfsopp0ScU1hYGF5h\nH0lw7zXenuDphnMeemdARCR6JtKhLglauHCh3bx5c7LLkCg1NDSwePHiIec4jkNBQUGfVcj+7Qt7\nA2uyVyETJVLbzF69q9DxDrPWWtLShl830L9N8dHbHnP6xbdEfLepa/sWdj1yPV6vl23bto34+0Xz\n97CvgX8n+78zMN7+TqaCWO+hpCbdR/cxxrxorR228Uu8D6yKpLTebRO9K867HrmeN25fzq5Hro+5\nv/hYkMhV6N4V9qGCe319/aCdYuTQpPo5Dze8MyAikkqiDu/GmAPGmFXDzPmGMWb/yMsSGT3jbdvE\ncEbaDWYo0bR27OjoCAf2aHq3S2xS+WAyqAOUiEisYll5N6Ff0cwTSWmjGVjHuzvuuGPYwP7KK6+E\nA3tGRkYCqxt/Uv2cR6q/MyAikmrivW3mSKArzl9TRFLcPffcEw7sX/nKVyLOufvuu8OBvaCgIMEV\njl+pcDB5KKn+zoCISKoZMrwbY07t/RW6lN/3Wp9fpxljLgMuBraOetUiknTNzc3hwH711VdHnHPu\nueeGA/tVV12V4AoF4nfOY6iHPPUd++Mf/xjTA6BS/Z0BEZFUM1yf9wbe7+1ugctCvyIxQA9wXVwq\nE5GU09XVNew2l5ycHHbv3p2giiQavec8qqurqampCfdRLy0tpaysbNjgHqkrUW8rxzvvvBNrLV1d\nwTdde3p6wmPV1dXDdiwqLy+nurqaQOidgcE6QI21B2eJiByq4cL7twmGdgN8k2CYfzbCvAMEH9D0\nf9bav8WzQBFJvmgOkqpDTGrrPedRUVER0+cN95Cn3gddTfJ+mMP/7RzSMqeSljmVns52AoEAS5Ys\n4dlnnx20j/94fHCWiMhIDBnerbU39v45tC3mF9baO0a7KBFJvmgC+4EDB6Lq2S7udXArx96OMJNz\n5zNp6arwvvnDMo/gn7+8jZ5P3kRPxzvhz9+3bx+fXryYpzZuHHQFfqTvDIiIjCfDrbyHWWuPGc1C\nRCT5jj/+eP7+978POaetrY2jjz46QRVJskXTyrGzuYmOv/0WsKRNymL6xbcMWJ0vLi4e8kFLh/rO\ngIjIeBNLn/e5xphLjTERf2obY7JD48fGrzwRGW2PP/54+ODpYMF906ZN4YOnCu7jS7StHMGSMXcR\nE46cqQctiYiMolje774B+AHQPsj4u8CtwP8baVEiMroaGhrCgf28886LOOeGG24IB/bx9uAqeV+0\nrRwhuDp/MD1oSUQkvmIJ74uBZ6y1+yINhq4/DeinvEgK+uc//xkO7KeddlrEObNmzQoH9u9973sJ\nrjA5hmqBKNG3cgQ9aElEJBFiCe+zgZZh5jjArEOuRuJCYUR69fT0hAP7YA+5KSgoCAf2HTt2JLjC\n5Kqvr6egoIDKykocx6GjoyPc5rCgoID6+vpkl5h00TzkqZcetCQiMvqiPrAKdANThplzOO/3hZck\nGKofczQ9l2VsUGvH4Q3XAjEQxSHL8WC4Vo4ZGRl0d3dz4MAB2hvXwFnf6DeuBy2JiMRXLCvvrwCf\nNcZMjDRojEkHzgG2xKMwid3BYWT6xbcw55q1TL/4lvCBseLiYq3Aj1G9K+xDBfeurq7wKvt4d3AL\nRB2yHFxvK0efz4fX6yUzMxOv14vP5+Nvf/sbv/nNb5iYnk5ncxP7//VWxNV5PWhJRCQ+YgnvDwNe\nYI0xZkbfgdDHa4A5wE/jV57EQmFk/CkpKRk2sL/xxhvhwD5p0qQEVpfaommBCDpk2au3leO2bdvY\ns2cP27Zto6KiAq/XyymnnMJTGzfi8Xjo2buHXY9czxu3L2fXI9eHg7setCQiEh+xhPf7gGeAYuA1\nY8zvjDFrjTG/A14DzgM2AffEv0yJhsLI+PCb3/wmHNhXr14dcc7GjRvDgT03NzfBFQal+tmLaFsg\n6pBldHpX52fMmDFgdd7v92u7nohInEQd3m2wzcBngQpgH1AILA393g18F/isPbgdgSSMwsjY9fLL\nL4cD+6mnnhpxzrXXXhsO7EuWLElwhf254SBotC0Qoz1kmeovVhLB6/Uye/bsiKvzIiISHzE919xa\nu89a+3XgaOCDwCdDv2dba/97sDaSkhjxDiOSXB0dHeHA/uEPf3jQeb2B/Qc/+EECqxucW85eRNsC\nMZpDlm54sSIiImNDTOG9l7W2x1q7xVr7u9DvPQDGmDRjTHF8S5RoxTOMSHJYa8OBPSsrK+Icj8cT\nDuypePDULWcvommBGM0hS7e8WBERkbHhkML7wYwxecaYmwj2eV8fj68psYtXGJHE++QnP4kxhrS0\nwf9K9vT0YK3lvffeS2BlsXPL2YveFoi9f2cO9ZClW16siIjI2HDI4d0Yc5gx5gJjzFNAM/ANYCbB\nQ62SBF6vlxtvvBEgYhgBuPHGG7X/NEWce+654VX2559/PuKc9vb28Ap7NL3bU4Gbzl4M1QIx2kOW\nbnmxIiIiY0PM4d0Yc6wx5nvAdmAtcAbwT+Bm4Fhr7ZnxLVGi5ThOOLxPmDqDtMypmAmTSMucyoSp\nwe6eN954o96+T6If/vCH4cD+xBNPRJzzj3/8IxzYDz/88ARXOHJuO3sxVAvEaLjpxYrEhw4ni0gy\nRRXejTETjDHLjDFPA68CPuBIgltkDFBnrf2mtXbb6JUqw+n79v2sK+5jzpcfxnvdOuZ8+WFmXXGf\n3r5Pkt27d4cD+1e/+tWIc37+85+HA3t+fn5iC4yz8Xb2wm0vVmRkdDhZRJJtyPBujJlnjKkEdgC1\nwGeAPwJfBmZaa5eNfokSLb19nzra2trCgX369OkR51xxxRXhwL506dIEVzh6xtvZi/H2YmU80+Fk\nEUkFE4YZ3wpYYBfwv8BD1lr/qFclh0Rv3yfX/v37mThx4pBz5s2bx6uvvpqgihLPcRyqqqrIzMwk\nEAjQ2dwUPm/RKzMzk89+9rN86lOfoq2tjezsbEpKSigvL09S1SNTXl5OdXU1gdCLlSmFy0jPyae7\ntYX2xrVj7sXKeHbw4eTeRZLJufOZtHQVretuItDcRHV1NRUVFUmuVkTGqmi2zVhgI7BOwT216e37\n5OhdYR8suF9++eXhFfaxHNz7bifYvXv3gPFp06ZRUlISfjJspC0Hqd5JJ5J4da2R1Kd3N0UkFQwX\n3lcRbP94OfC8MWaLMeZ6Y8zM0S9NYqW37xPntttuC4f2wezfvx9rLT/60Y8SWFlyDLedAGDPnj1s\n2LCBPXv2DLrl4LXXXnPlloN4dK2R1Kd3N0UkFQwZ3q2137HWHgucBTwGzAUqAMcY86QxZnkCapQo\njbe9xom2atWqcGC/9tprI87ZtWtXeJX9sMMOS3CFyRNNr/M9e/bQ0dEx5Jyenp6IB6rd0N1jpF1r\nJPXp3U0RSQVRdZux1v7KWvt5YA7wdWAbwUBfQ3BbzUeMMQtGrUqJit6+j7/Vq1eHA/vNN988YHzK\nlCls27YtHNinTZuWhCqTL9rtBNHMOXjLgbp7SKrQu5sikgpi6vNurd1tra2w1h5HsL/7z4F9wELg\nBWPMH40x7jx1Nkbo7fuRe+edd8KBvfeH9cEef/xxrLW8++67ejFE9NsJopnTd8uBuntIKtG7myKS\nCg75CavW2k3W2guBXOB64O/AScAdcapNDpHevo9dIBAIB/Yjjzwy4pzzzz8/vMJ+zjnnJLjC1Bbt\ndoJo5vTdchDNdhw9u0ASRe9uikgqOOTw3sta22atvdVaewJQRHArjUjKs9aGA/tgTzI1xoQD+2OP\nPZbgCt0j2u0E0czpu+VA3T0k1ejdTRFJthGH976stQ3W2kvi+TVF4m3q1KkYY0hLi/x///POOy8c\n2Ht6eiLOkf6i2U6QlZVFZmbmkHPS0tL6bTlQdw9JRXp3U0SSabiHNImMCRs3buTss88eck5nZyeT\nJ09OUEVjS+92guLiYgIRHszUu50AGHLOcccd1y8AZWdn4zgO3btbmJw7f8D3VXcPEREZb+K68p7q\njDFLjDFbjTGvGWNuSHY9Mroef/zx8LaYwYL7m2++GV5lV3AfmWi2Eww35+DtS+ruISIi0p+x1ia7\nhoQwxhwGvEqwS852oAkotdZuGexzFi5caDdv3pygCmWkGhoaOPzww1m4cOGQ87Zu3crxxx+foKok\nFg0NDSxevDj8seM4FBQUhA+tTilcRnpOPt2tLbQ3rg0fEvT7/QO2LDiOQ1VVFbW1tbS1tZGdnU1J\nSQnl5eXa3jCKDr6H4j66h2OD7qP7GGNetNYOHWIYX9tmPgq8Zq19HcAYUwsUA4OGd3GHPXv24PF4\nhpyzadMmHSRzoWi34xwcxuvr68MtJnv19oavrq6mrq5O/38QERFXGk/bZmYDb/T5eHvomrjQ/v37\nOf300zHGDBrcV6xYEd4So6DmXrF291BveBERGcvG07aZzwNLrLX/Efr4C8DHrLX/edC8K4ArAKZP\nn76gt1WdpIZvfetbPPfcc4OOp6WlsWnTpgRWJPEUCASGfRdlODt27GDnzp2kTcpiwpEzB4zv/9db\n9N0yj14AAB/iSURBVOzdw4wZM5g9e+y+fu/u7qa1tZW3336b/fv3M2HCBI466ihycnJIT08fte8b\nj3soyaV7ODboPrrPaaedpm0zB9kBzOnzcW7oWj/W2vuA+yC45137xZLviiuu4P777x90vKysjLvu\nuotnn31W+/tcLh57NP//9u49zKqzPvT490cC4TIhJuGSC26wMaY4vURzeeDEC8FL0rQ6KkkE00o9\nPZoKttq0zUR7OMbDaTOSp41HC/potURPAsUQnbSaaMuUljZiMTEaB6PJGNiSIBejkgkEDLznj7Vm\n2DPsYRgYZu818/08zzx7z7vevdZvr3dv+O13fuvd06dPp1wuM/WG2xk77ch/4p7f9iw77rqZUqnE\n1q1bT+hY9aqtrY158+b1KBvq0lVqdLL+GmWdbfE5hsOD4zh8jaTkfRNwYUS8hCxpnw+8o7YhqS+P\nPfYY1157Le3t7X322bt3L+PGjRvCqFQEI31t+N5lQxNnXc+YKTM4sHMLezauobNjE01NTVUv8pUk\n1b8RU/OeUnoBeB/wNeD7wJqUUt+ZoYbcww8/3L2048yZM6sm7tu3b++uYzdxVzVda74f2Lml6vbh\nvjb88uXLuxP3yfOWMHbaTEaNGcfYaTOZPG9Jd93/ihUrah2qJOk4jJjkHSCl9NWU0stSSheklP6y\n1vEoW2e9K2G/5JJLjth+1VVX8fjjj3cn7Oecc04NotRgK5fLNDc3M336dCZMmMD06dNpbm7mwIED\nJ7zvkb42fNd1OhNnXU9Ez3/iI0YxcdZ1AKxatWrIY5MknbiRVDajOrF//34mTpx41ERtw4YNvOpV\nrxrCqDRUjraM4znnnMOpp556QvXYixcvZsWKFXR2bGLX2qV9rg2/aNGiwXg6dWeklw1J0nBn8q4h\ncejQIS6++GIeffTRPvvcdttt3HKLX3w7nPVXj33o0KETrsc+3rXhh4tJkyZRLpc5sHMLY6fNPGL7\ncC8bkqThbkSVzWjoXXfddUQEp5xyStXEfcqUKd0lMSbuw19/9dijTpswKPXYA10bfjgZ6WVDkjTc\nmbxr0N10003ddez33HPPEdsXLlzIwYMHSSmxY8eOGkSoWumvHvuUCWcCg1OPXSqVaGlpYevWrTz3\n3HNs3bqVlpaWYTvj3mXx4sU0NDSwLy8ben7bZg7t38vz2zaza+3SYV82JEnDnWUzGhQPPfQQl156\n9O8VeOaZZzjzzDOHKKL6Uy6XWb58OatXr2b37t1MmjSJ+fPns3jx4mGfUHbprx47Ro/p0U8DN9LL\nhiRpuHPmXcft29/+dvcMe1+J+5NPPtldFjOSE/e2tjYaGxtZtmwZ5XKZvXv3dl+k2djYSFtbW61D\nHBL9LeOYfnmgRz8dn5FcNiRJw53JuwbkmWee6U7YX/nKV1bts2HDhu6EfcaMGUMbYB3qfZHm1Btu\n58V/8kWm3nB795rbTU1NlMvlWod60vVXj33wuZ8B1mMPhpFaNiRJw53Ju/r1wgsvcN555xERnH32\n2VX73Hnnnd0Ju0s89uSX5hzWXz32of3PWY8tSdJRmLyrqpQSb3zjG4kIRo8ezfbt24/oc+ONN3Yn\n7O985ztrEGUx+KU5h3XVY3cl8Dvuupkff+x6dtx1M/s6NjFq1CjrsSVJOgovWFUP733ve/nUpz51\n1D6HDh0iIoYoouLzS3N66qrHXrFiBatWreq+eHfBggU0NjZajy1J0lE48y5uu+227jr2aol7U1MT\nBw4c6J5lN3EfmP4u0hyJX5rTVz32mDFjah2aJEl1zeR9hNq8eXN3wv6hD32oap+nn36alBJf/vKX\nGT169BBHOHz4pTmSJGmwmLyPIE8//XR3wt7Y2Fi1T3t7e/cM+7nnnjvEEQ5PfmmOJEkaLNa8D3P7\n9u3j1a9+NQ899FCffe6//36uvvrqIYxqZPFLcyRJ0mBx5n0YSinxjW98g4hg/PjxVRP3T3ziE90z\n7CbuJ59fmiNJkgaDM+/DyOOPP86TTz7JokWL6OjoOGL7bbfdxi233FKDyASHL9JsaWmpdSiSJKmg\nnHkvuAcffJAFCxbwile8gpe97GXs2LGDjo4Ozj33XM466yze9KY3cfDgQVJKJu6SJEkF58x7Af3w\nhz/k7W9/O4888kiP9jPOOINx48axYcMGZs+ezSmnnFKjCCVJknQymLwXRGdnJ/fddx9f+MIXeOCB\nB47YvmbNGt785jdz2mmn1SA6SZIkDQWT9zp24MABvv71r7NmzRpmz559xFKCb3jDG1i5ciXnnXde\njSKUJEnSUDJ5r0O33347N998c4+2K664gjlz5nDttddy7bXXMnXq1BpFJ0mSpFoxea8z9957b4/E\n/aKLLmLhwoVcc8013HjjjTWMTJIkSbVm8l5nLrroIk4//XSeffZZ7r77bhYsWFDrkCRJklQnTN7r\nTGNjI3v27Kl1GJIkSapDrvOuIVcul2lubmb69OlMmDCB6dOn09zcTLlcrnVokiRJdc3kXUOqra2N\nxsZGli1bRrlcZu/evZTLZZYtW0ZjYyNtbW21DlGSJKluWTajIVMul2lqaqKzs5NxF1zGxFnXM2bK\nDA7s3MKejWvo7NhEU1MT7e3tlEqlWocrSZJUd5x515BZvnx5d+I+ed4Sxk6byagx4xg7bSaT5y1h\n3AWX0dnZyYoVK2odqiRJUl0yedeQWb16NQATZ11PRM+XXsQoJs66DoBVq1YNeWySJElFYPKuIbN7\n924AxkyZUXX7mMkzevSTJElSTybvGjKTJk0C4MDOLVW3H9i1pUc/SZIk9WTyriEzf/58APZsXENK\nh3psS+kQezZ+EcAvppIkSeqDybuGzOLFi2loaGBfxyZ2rV3K89s2c2j/Xp7ftplda5eyr2MTDQ0N\nLFq0qNahSpIk1SWXitSQKZVKtLa2ZstFdmxiX8emHtsbGhpobW11mUhJkqQ+OPOuITV37lza29tp\nbm6mVCoxfvx4SqUSzc3NtLe3M3fu3FqHKEmSVLecedeQK5VKtLS00NLSUutQJEmSCsWZd0mSJKkg\nTN4lSZKkgjB5lyRJkgrC5F2SJEkqCJN3SZIkqSBM3iVJkqSCMHmXJEmSCsLkXZIkSSoIk3dJkiSp\nIEzeJUmSpIIweZckSZIKwuRdkiRJKgiTd0mSJKkgTN4lSZKkgjB5lyRJkgrC5F2SJEkqCJN3SZIk\nqSBM3iVJkqSCMHmXJEmSCsLkXZIkSSoIk3dJkiSpIEzeJUmSpIIweZckSZIKwuRdkiRJKgiTd0mS\nJKkgTN4lSZKkgjB5lyRJkgrC5F2SJEkqCJN3SZIkqSBM3iVJkqSCMHmXJEmSCsLkXZIkSSoIk3dJ\nkiSpIEzeJUmSpIIweZckSZIKom6T94i4LiLaI+JQRFzaa9sHI+KJiPhBRFxV0X5JRDyab/t4RETe\nflpE/EPe/s2ImDG0z0aSJEk6cXWbvAPfA94G/HtlY0S8HJgPNAJXAysi4pR88yeBdwMX5j9X5+1/\nAPwspfRS4A7goyc9ekmSJGmQ1W3ynlL6fkrpB1U2NQGrU0r7U0pPAk8Al0fEucDElNLGlFICPg+8\npeIxd+b37wFe1zUrL0mSJBXFqbUO4DicD2ys+H1b3vbL/H7v9q7H/BggpfRCRPwCOBvY3XvnEfEe\n4D0AU6dOZf369YMcvk6Wzs5Ox6vgHMPicwyLzzEcHhzH4aumyXtE/AtwTpVNf5FSah3qeABSSp8G\nPg1w6aWXpjlz5tQiDB2H9evXM5LGq1wus3z5clavXs3u3buZNGkS8+fPZ/HixZRKpVqHd1xG2hgO\nR45h8TmGw4PjOHzVNHlPKb3+OB72FPDiit+n5W1P5fd7t1c+ZltEnAqcAfz0OI4t1YW2tjaampro\n7OzsbiuXyyxbtowVK1bQ2trK3LlzaxihJEk6Geq25v0o7gPm5yvIvITswtT/SiltB/ZExKy8nv2d\nQGvFYxbm968F2vK6eKlwyuVyd+I+7oLLmHrD7bz4T77I1BtuZ9wFl9HZ2UlTUxPlcrnWoUqSpEFW\nt8l7RLw1IrYBs4GvRMTXAFJK7cAaYDPwALA4pXQwf9gi4O/ILmLtAO7P2z8LnB0RTwA3AbcM2ROR\nBtny5cu7E/fJ85YwdtpMRo0Zx9hpM5k8b0l3Ar9ixYpahypJkgZZ3SbvKaUvpZSmpZROSylNTSld\nVbHtL1NKF6SULkop3V/R/q2U0q/l297XNbueUno+pXRdSumlKaXLU0o/qsVzkgbD6tWrAZg463oi\ner6FI0YxcdZ1AKxatWrIY5MkSSdX3SbvkqrbvTtbJGnMlBlVt4+ZPKNHP0mSNHyYvEsFM2nSJAAO\n7NxSdfuBXVt69JMkScOHybtUMPPnzwdgz8Y1pHSox7aUDrFn4xcBWLBgwZDHJkmSTi6Td6lgFi9e\nTENDA/s6NrFr7VKe37aZQ/v38vy2zexau5R9HZtoaGhg0aJFtQ5VkiQNsiJ+w6o0opVKJVpbW7Pl\nIjs2sa9jU4/tDQ0NtLa2FvaLmiRJUt+ceZcKaO7cubS3t9Pc3EypVGL8+PGUSiWam5tpb2/3C5ok\nSRqmnHmXCqpUKtHS0kJLS0utQ5EkSUPEmXdJkiSpIEzeJUmSpIIweZckSZIKwuRdkiRJKgiTd0mS\nJKkgTN4lSZKkgjB5lyRJkgrC5F2SJEkqCJN3SZIkqSBM3iVJkqSCMHmXJEmSCsLkXZIkSSoIk3dJ\nkiSpIEzeJUmSpIIweZckSZIKwuRdkiRJKgiT9zpSLpdpbm5m+vTpTJgwgenTp9Pc3Ey5XK51aJIk\nSaoDJu91oq2tjcbGRpYtW0a5XGbv3r2Uy2WWLVtGY2MjbW1ttQ5RkiRJNXZqrQNQNuPe1NREZ2cn\n4y64jImzrmfMlBkc2LmFPRvX0NmxiaamJtrb2ymVSrUOV5IkSTXizHsdWL58eXfiPnneEsZOm8mo\nMeMYO20mk+ctYdwFl9HZ2cmKFStqHaokSZJqyOS9DqxevRqAibOuJ6LnkESMYuKs6wBYtWrVkMcm\nSZKk+mHyXgd2794NwJgpM6puHzN5Ro9+kiRJGplM3uvApEmTADiwc0vV7Qd2benRT5IkSSOTyXsd\nmD9/PgB7Nq4hpUM9tqV0iD0bvwjAggULhjw2SZIk1Q+T9zqwePFiGhoa2NexiV1rl/L8ts0c2r+X\n57dtZtfapezr2ERDQwOLFi2qdaiSJEmqIZeKrAOlUonW1tZsuciOTezr2NRje0NDA62trS4TKUmS\nNMI5814n5s6dS3t7O83NzZRKJcaPH0+pVKK5uZn29nbmzp1b6xAlSZJUY86815FSqURLSwstLS21\nDkWSJEl1yJl3SZIkqSBM3iVJkqSCMHmXJEmSCsLkXZIkSSoIk3dJkiSpIEzeJUmSpIIweZckSZIK\nwuRdkiRJKgiTd0mSJKkgTN4lSZKkgjB5lyRJkgrC5F2SJEkqCJN3SZIkqSAipVTrGOpWROwCttY6\nDh2zScDuWgehE+IYFp9jWHyO4fDgOBbP9JTS5P46mbxr2IiIb6WULq11HDp+jmHxOYbF5xgOD47j\n8GXZjCRJklQQJu+SJElSQZi8azj5dK0D0AlzDIvPMSw+x3B4cByHKWveJUmSpIJw5l2SJEkqCJN3\nSZIkqSBM3lV4EXF1RPwgIp6IiFtqHY/6FhFbIuLRiHgkIr6Vt50VEf8cEY/nt2dW9P9gPq4/iIir\nahf5yBYRn4uInRHxvYq2AY9bRFySj/8TEfHxiIihfi4jVR9jeGtEPJW/Hx+JiGsqtjmGdSYiXhwR\n/xoRmyOiPSLen7f7XhxhTN5VaBFxCrAc+C3g5cCCiHh5baNSP65MKV1csf7wLcC6lNKFwLr8d/Jx\nnA80AlcDK/Lx1tBbSTYGlY5n3D4JvBu4MP/pvU+dPCupfr7vyN+PF6eUvgqOYR17AfjTlNLLgVnA\n4nysfC+OMCbvKrrLgSdSSj9KKR0AVgNNNY5JA9ME3JnfvxN4S0X76pTS/pTSk8ATZOOtIZZS+nfg\nmV7NAxq3iDgXmJhS2piylRI+X/EYnWR9jGFfHMM6lFLanlJ6OL//LPB94Hx8L444Ju8quvOBH1f8\nvi1vU31KwL9ExEMR8Z68bWpKaXt+/yfA1Py+Y1vfBjpu5+f3e7ertv4oIr6bl9V0lVs4hnUuImYA\nrwC+ie/FEcfkXdJQelVK6WKyMqfFEfGayo35LJDr1xaM41ZYnwR+BbgY2A78dW3D0bGIiAZgLfCB\nlNKeym2+F0cGk3cV3VPAiyt+n5a3qQ6llJ7Kb3cCXyIrg9mR/xmX/HZn3t2xrW8DHben8vu921Uj\nKaUdKaWDKaVDwGc4XJbmGNapiBhNlrjflVK6N2/2vTjCmLyr6DYBF0bESyJiDNnFOffVOCZVERET\nIuL0rvvAG4HvkY3XwrzbQqA1v38fMD8iTouIl5BdVPVfQxu1jmJA45b/WX9PRMzKV7Z4Z8VjVANd\nCV/urWTvR3AM61J+zj8LfD+l9DcVm3wvjjCn1joA6USklF6IiPcBXwNOAT6XUmqvcViqbirwpXxF\nslOBu1NKD0TEJmBNRPwBsBW4HiCl1B4Ra4DNZKssLE4pHaxN6CNbRKwC5gCTImIb8GGghYGP2yKy\nVU/GAffnPxoCfYzhnIi4mKzMYgtwIziGdewK4PeARyPikbztQ/heHHEiK4+SJEmSVO8sm5EkSZIK\nwuRdkiRJKgiTd0mSJKkgTN4lSZKkgjB5lyRJkgrC5F1SIUTEjIhIEbGyV/vKvH1GTQIboHqLNyJu\nzeOZU+tYBktfr5VjeNz6iBiUJdiqjfPxxlVEETExIj4eEVsi4oX8eV8cEXPy+7fWOkapqEzeJXXL\n/1Ot/DkYEbsjoi0i3lHr+E6GkZRQjXT19sFpmFsG/BHwKHAb8BHgJ311HswPTtJw55c0SarmI/nt\naOBXgSbgyoi4NKV0U+3CquqDZF9S4td7q8tTwEzgF7UOpJd6jetk+B3ghymlN1U2RsQesnOwuyZR\nScOAybukI6SUbq38PSJeB/wz8IGI+HhKaUst4qom/6rv7bWOQ/UjpfRL4LFax9FbvcZ1kpwH/Hvv\nxpTSXkbOOZBOCstmJPUrpbSO7D/cAC6DnuUmEfGyiPiHiNgZEYcq66cj4qyIuC0ivh8R+yLiFxGx\nLiLeWO1YEXF6RPxNRGyLiOcj4rGIuIk+/r06WilERFyex/VUROyPiO0R8fWIuD7ffivwZN59Ya+S\nod/vta+rIuKreRnR/ojoiIjbI+JFfcT1+ojYEBHPRcQzEfHliPjVo5zmavt4LCIORMSkPrY357G+\nr6Ltyoj4dERsjog9+Tn/XkR8OCLGHuNxj1pKdLQSh4GepyqPvzE/9rt7tb8rb98bEaf12vbN/LUy\nrq/483gX5r8+WTHOW6rEcGpEfCgiHs+fw48j4qMRMeZYnsNRnlu/123kz//R/PnsyMfyjD72Ny0i\n/jYifpTH+dOIuC8iLqvS97yI+F8R8Z8R8ZP8dfV0RNwdES8/WqxHe39XeVzXayOA11ac5/X59h41\n713HAV6b/556P0ZST868SzpWkd/2TtouAL4J/BC4CxgH7AGIiOnAemAGsAF4AJhA9if1ByLixpTS\nZ7oPkCVl68g+IHwn39+LgCXk/7kfc7BZ8vdJ4CBwH/A4MAW4FFgErMljexHw/vx4X67YxSMV+/ow\ncCvwDPBPwE7gN4A/A66JiNkppT0V/a8F/gE4kN9uB14FfAP47gCexp3AXwELgE9U2b4wP8bdFW3N\nZKVODwJfAcYCV+Txz4mI16eUDg4ghmM20PPUh3X57euAz1S0vy6/HQfMJhs78sT2EmBDSmnfUfb7\nEeAtwG8C/xf4ed7+8yp97wZeDdxP9lq+BriZ7PXzrn7iPxHLgKuAfwS+DlwJvBt4KTC3smNEvDLv\ncxbwNeBeYBLZc/yPiHhrSumrFQ95DXAL8K/AWqATuBC4FnhzRFyRUvpOlZj6fH/3YSXZ2HwY2Jr/\nDrClj/4/Jxub3wemc7hk72iPkUa2lJI//vjjDyklyBLzVKX99cCh/Gd63jajqz/wV33sb33+mPm9\n2l9ElhzvA6ZWtH8o399aYFRF+0vIEsIErOy1r5V5+4yKtpcDv8wf01glrmkV92dU22/F9ivz7Q8C\nL+q17ffzbXdUtDUAP82Pf2mv/ndUnLMZ1Y7XO06yDx/fqrLtsq5z1av9V4Co0n9p3v/tvdpvzdvn\nDOCcrO/9OhnoeerneW8lS/yjou1pssT+ILC0or0p3/eS/uKv9lqp9ryAh4CzKtonAE/kxz7nGJ9D\ntddlf3GVgVJF+6lkpScJuLxX+xPA88Bre+3rPLLa+u3AaRXtU4DTq8T5m2SJ/P292rti7fP93c/z\nT8D6Ku1z8m239vea8scff6r/WDYj6QiRLR94a0T8ZUTcQzZjHsDHUkpbe3XfQc/Zsq59/CbZbPna\nlNLqym0ppZ+TzcyNBeZVbHoXWbJ/c0rpUEX/J4GPD+ApvJcswVmaUmrvvTGltG0A+/rj/PbdedyV\n+1lJ9iHkhormJrLZ0LtTSt/qta9bGcDFinmc64BLIqKx1+auEpA7ez3mRymlaiUtd+S3Vx3r8Qdo\noOfpaNqAycCvA+RlHecC9wAPc3gWnor76xg8zSmlZ7p+SSk9RzbrPIrsLzcny/9OKZUrjvsC8Pf5\nr5dX9PttshnxT6SU/q1yBymlp8lm8M+h4jyllHamlJ7tfcCUzba3kV2QPrpKTFXf35Jqx7IZSdV8\nOL9NZH/W3gB8NqX0/6r0/U5KaX+V9tn57RlRfU3nyfntTMhq3cnKA36cUuqo0n99RVz9mZXf3n+M\n/Y9mNtks+nURcV2V7WOAyRFxdkrpp8Ar8/Z/690xpfSLiHiEgZUArQTeQJas3wyQ114vIJudriyN\nICImkJUBvRV4GXA6h0ueAM4fwLEHYqDn6WjayGbrX0dWZtRVMrKObEb4pog4PU9G55LNHP/XCT+D\nw3p/6AL4cX575iAe53iP2/Xemt7He+vC/HYmFa+PiPht4A/JPoBM4sgcYBJHXvzd1/tbUo2YvEs6\nQkop+u/Vra+1m8/Ob9+Q//SlIb/tuihvxwCPU03XxZGDsXzk2WT/Vvb3waGrXGYwnwfAl8hqjH83\nIj6Ysnr13yGb3f9YPjsLQD5z2kY2S/s9snr7XWRJNflz6HGx5yAa6Hk6msq69zvy220ppR9GxDqy\nDzGvjYhvAY3AVyvPw4nq/ZeDXNf+Txms41RxrMftem9V+5BUqeu9RUS8H/gY8DOylaPKwF6yD+hd\n1wJUe20M9PUq6SQzeZd0ovr6YpWu8pD3p5SOpeSlq//UPrafM4CYupKg8znxZel+QVZ/f9YA+sPg\nPA9SSvsiYg3wP8g+BD1AHyUzZCU7l5PVVPe4sDIizuXY/3LRVbLU1/8R1VaOGeh56lNK6emI+AHw\nmvwi5jlAa775P8gu0n09MDFvazvRYxZM12usKaV0X3+dI+JUspKtnwCvTNnyqpXbZ1d7XM4vTpLq\njDXvkk6Wjfntq4+lc14C8QRwfkRcUKXLnOM49m8dQ9+ulVf6mlHdCJxZpea8Lw/nt0eUxuQro1x8\njPuptDK/XRgRk8me13dTSo/06vfS/PbeKvsYSKnOz/LbF/feEBETycpxehvoeerPOrKSn/eSfVhY\nB93rhG8km42vLKc5Fv2NdVEM6L1FVg7zIuDBKol7A4dLvWrpIEBEFH1spJPO5F3SSZFfrLkBeFtE\n/PdqfSLi1yNiSkXT35P9u/TRiBhV0e8lHL4g8lh8kqzcYEkfa1hPq/j1Z2Szi6U+9tV1oednIuK8\nKvuaEBGzKppa832+IyJ6X9x4K4fLao5ZSuk/yZa6bCKrWR7N4YS+0pb8dk6vGH8F+OgAjvcs2V8s\nrqg8f3li9TdkywX2NtDz1J+u2fQP5rfrem37NeDNZCU41ZY4rKarXKevsS6KVqADWBwR11TrEBGz\nI2J8/utOshKZS/JkvavPaLJlM6t+j8AQGy5jI510ls1IOpneQZZofTYi/phsveifky2B+BtkCdhs\nsuQC4K/J6m/nAQ9HxNfIZgyvJ1sy783HctCU0uaIWAR8Cvh2RLSSJb9nky2xuIdsaUNSSp0R8U3g\n1RFxF9l61geB+1JK300prYuIW4DbgMcj4qtkX+zUQLYu9WvJSjmurtjfe8jqzTdEROU677+WP4/X\nDOgsZj5PttzjErIPJndV6fOPZH+9uCkifh34Nlky9Dtka74PJDG6Hfgs8J8R8UWyZQmvJPvg8B2y\nGuluAz1Px+Bfycp3pgCP5auodFlH9kFoMnBPH6vrVLMO+HOyDxhrgWeBn6eU/vYYH18XUkq/jIi3\nka3v/pWIeJBsNZ+9ZH8tuYxsydBzgb0ppUMR8XGydd4fzd8PY8jG8yyyc33l0D+THtaR1fDfm792\n9gFbU0pfqG1YUv1x5l3SSZMvdXgJ8BdkCfENZDPo/43sgrkbgUcr+u8nq2W+gywxez9Z0vd/gD8Z\n4LE/Q5Yw/xPZTPSfkyX/u4Dlvbr/HllyezVZXfhSKkoJUkofJUu4v0L2hUcfIEs0zgc+DfzPXse+\nJ9/XQ2QfPP6QbM352Rz+RteB+jxZMjsaeCCltLN3h3xJw7lkXzLUSHaufyN/Pr87kIOllD5HVmf/\nNFmN/fVka7hfQfULKwd8nvo5/jMc/qKs3jXt3wSe62Pb0fb5NeBPyS7g/QDZefmzY318PUkpfZfs\nA9RHyf6a8y6yEqNLyD60/R6wu+IhS8ie+z6y993byFa3uZzsvVhrf0f2we8MsguSlwJ/UNOIpDoV\nxz5hIUmSJKmWnHmXJEmSCsLkXZIkSSoIk3dJkiSpIEzeJUmSpIIweZckSZIKwuRdkiRJKgiTd0mS\nJKkgTN4lSZKkgjB5lyRJkgri/wOX3gxwzkuAeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998b91be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel(\"Predicted value with linear fit\",fontsize=20)\n",
    "plt.ylabel(\"Actual y-values\",fontsize=20)\n",
    "plt.grid(1)\n",
    "plt.scatter(y_pred_linear,y_linear,edgecolors=(0,0,0),lw=2,s=80)\n",
    "plt.plot(y_pred_linear,y_pred_linear, 'k--', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create polynomial features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(3,include_bias=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Feature1', 'Feature2', 'Feature3', 'Feature4', 'Feature5', 'Feature1^2', 'Feature1 Feature2', 'Feature1 Feature3', 'Feature1 Feature4', 'Feature1 Feature5', 'Feature2^2', 'Feature2 Feature3', 'Feature2 Feature4', 'Feature2 Feature5', 'Feature3^2', 'Feature3 Feature4', 'Feature3 Feature5', 'Feature4^2', 'Feature4 Feature5', 'Feature5^2', 'Feature1^3', 'Feature1^2 Feature2', 'Feature1^2 Feature3', 'Feature1^2 Feature4', 'Feature1^2 Feature5', 'Feature1 Feature2^2', 'Feature1 Feature2 Feature3', 'Feature1 Feature2 Feature4', 'Feature1 Feature2 Feature5', 'Feature1 Feature3^2', 'Feature1 Feature3 Feature4', 'Feature1 Feature3 Feature5', 'Feature1 Feature4^2', 'Feature1 Feature4 Feature5', 'Feature1 Feature5^2', 'Feature2^3', 'Feature2^2 Feature3', 'Feature2^2 Feature4', 'Feature2^2 Feature5', 'Feature2 Feature3^2', 'Feature2 Feature3 Feature4', 'Feature2 Feature3 Feature5', 'Feature2 Feature4^2', 'Feature2 Feature4 Feature5', 'Feature2 Feature5^2', 'Feature3^3', 'Feature3^2 Feature4', 'Feature3^2 Feature5', 'Feature3 Feature4^2', 'Feature3 Feature4 Feature5', 'Feature3 Feature5^2', 'Feature4^3', 'Feature4^2 Feature5', 'Feature4 Feature5^2', 'Feature5^3']\n",
      "55\n"
     ]
    }
   ],
   "source": [
    "X_poly = poly.fit_transform(X)\n",
    "X_poly_feature_name = poly.get_feature_names(['Feature'+str(l) for l in range(1,6)])\n",
    "print(X_poly_feature_name)\n",
    "print(len(X_poly_feature_name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "      <th>Feature1^2</th>\n",
       "      <th>Feature1 Feature2</th>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <th>...</th>\n",
       "      <th>Feature3^3</th>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <th>Feature4^3</th>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <th>Feature5^3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "      <td>238.813659</td>\n",
       "      <td>275.152347</td>\n",
       "      <td>-371.136432</td>\n",
       "      <td>162.200862</td>\n",
       "      <td>88.433008</td>\n",
       "      <td>...</td>\n",
       "      <td>13851.985264</td>\n",
       "      <td>-6053.849078</td>\n",
       "      <td>-3300.599522</td>\n",
       "      <td>2645.764341</td>\n",
       "      <td>1442.488639</td>\n",
       "      <td>786.454576</td>\n",
       "      <td>-1156.300538</td>\n",
       "      <td>-630.422885</td>\n",
       "      <td>-343.710827</td>\n",
       "      <td>-187.393471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "      <td>450.364147</td>\n",
       "      <td>242.927223</td>\n",
       "      <td>-79.783161</td>\n",
       "      <td>-7.401034</td>\n",
       "      <td>269.419924</td>\n",
       "      <td>...</td>\n",
       "      <td>53.135896</td>\n",
       "      <td>4.929117</td>\n",
       "      <td>-179.434718</td>\n",
       "      <td>0.457246</td>\n",
       "      <td>-16.645146</td>\n",
       "      <td>605.933472</td>\n",
       "      <td>0.042416</td>\n",
       "      <td>-1.544076</td>\n",
       "      <td>56.209028</td>\n",
       "      <td>-2046.178007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "      <td>187.553677</td>\n",
       "      <td>98.312514</td>\n",
       "      <td>263.630971</td>\n",
       "      <td>-133.846016</td>\n",
       "      <td>-2.679000</td>\n",
       "      <td>...</td>\n",
       "      <td>7133.471192</td>\n",
       "      <td>-3621.678794</td>\n",
       "      <td>-72.489856</td>\n",
       "      <td>1838.734178</td>\n",
       "      <td>36.803257</td>\n",
       "      <td>0.736637</td>\n",
       "      <td>-933.529330</td>\n",
       "      <td>-18.685094</td>\n",
       "      <td>-0.373992</td>\n",
       "      <td>-0.007486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "      <td>390.726434</td>\n",
       "      <td>218.878557</td>\n",
       "      <td>20.456610</td>\n",
       "      <td>195.477657</td>\n",
       "      <td>1.805316</td>\n",
       "      <td>...</td>\n",
       "      <td>1.108388</td>\n",
       "      <td>10.591446</td>\n",
       "      <td>0.097816</td>\n",
       "      <td>101.208905</td>\n",
       "      <td>0.934705</td>\n",
       "      <td>0.008632</td>\n",
       "      <td>967.124046</td>\n",
       "      <td>8.931784</td>\n",
       "      <td>0.082489</td>\n",
       "      <td>0.000762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "      <td>28.496841</td>\n",
       "      <td>-71.163840</td>\n",
       "      <td>26.038690</td>\n",
       "      <td>-3.066398</td>\n",
       "      <td>-44.069336</td>\n",
       "      <td>...</td>\n",
       "      <td>-116.054593</td>\n",
       "      <td>13.666955</td>\n",
       "      <td>196.417286</td>\n",
       "      <td>-1.609464</td>\n",
       "      <td>-23.130719</td>\n",
       "      <td>-332.427601</td>\n",
       "      <td>0.189536</td>\n",
       "      <td>2.723946</td>\n",
       "      <td>39.147722</td>\n",
       "      <td>562.619066</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 55 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5  Feature1^2  \\\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487  238.813659   \n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441  450.364147   \n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619  187.553677   \n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331  390.726434   \n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401   28.496841   \n",
       "\n",
       "   Feature1 Feature2  Feature1 Feature3  Feature1 Feature4  Feature1 Feature5  \\\n",
       "0         275.152347        -371.136432         162.200862          88.433008   \n",
       "1         242.927223         -79.783161          -7.401034         269.419924   \n",
       "2          98.312514         263.630971        -133.846016          -2.679000   \n",
       "3         218.878557          20.456610         195.477657           1.805316   \n",
       "4         -71.163840          26.038690          -3.066398         -44.069336   \n",
       "\n",
       "      ...         Feature3^3  Feature3^2 Feature4  Feature3^2 Feature5  \\\n",
       "0     ...       13851.985264         -6053.849078         -3300.599522   \n",
       "1     ...          53.135896             4.929117          -179.434718   \n",
       "2     ...        7133.471192         -3621.678794           -72.489856   \n",
       "3     ...           1.108388            10.591446             0.097816   \n",
       "4     ...        -116.054593            13.666955           196.417286   \n",
       "\n",
       "   Feature3 Feature4^2  Feature3 Feature4 Feature5  Feature3 Feature5^2  \\\n",
       "0          2645.764341                 1442.488639           786.454576   \n",
       "1             0.457246                  -16.645146           605.933472   \n",
       "2          1838.734178                   36.803257             0.736637   \n",
       "3           101.208905                    0.934705             0.008632   \n",
       "4            -1.609464                  -23.130719          -332.427601   \n",
       "\n",
       "    Feature4^3  Feature4^2 Feature5  Feature4 Feature5^2   Feature5^3  \n",
       "0 -1156.300538          -630.422885          -343.710827  -187.393471  \n",
       "1     0.042416            -1.544076            56.209028 -2046.178007  \n",
       "2  -933.529330           -18.685094            -0.373992    -0.007486  \n",
       "3   967.124046             8.931784             0.082489     0.000762  \n",
       "4     0.189536             2.723946            39.147722   562.619066  \n",
       "\n",
       "[5 rows x 55 columns]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_poly = pd.DataFrame(X_poly, columns=X_poly_feature_name)\n",
    "df_poly.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "      <th>Feature1^2</th>\n",
       "      <th>Feature1 Feature2</th>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <th>...</th>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <th>Feature4^3</th>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <th>Feature5^3</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "      <td>238.813659</td>\n",
       "      <td>275.152347</td>\n",
       "      <td>-371.136432</td>\n",
       "      <td>162.200862</td>\n",
       "      <td>88.433008</td>\n",
       "      <td>...</td>\n",
       "      <td>-6053.849078</td>\n",
       "      <td>-3300.599522</td>\n",
       "      <td>2645.764341</td>\n",
       "      <td>1442.488639</td>\n",
       "      <td>786.454576</td>\n",
       "      <td>-1156.300538</td>\n",
       "      <td>-630.422885</td>\n",
       "      <td>-343.710827</td>\n",
       "      <td>-187.393471</td>\n",
       "      <td>-431.953540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "      <td>450.364147</td>\n",
       "      <td>242.927223</td>\n",
       "      <td>-79.783161</td>\n",
       "      <td>-7.401034</td>\n",
       "      <td>269.419924</td>\n",
       "      <td>...</td>\n",
       "      <td>4.929117</td>\n",
       "      <td>-179.434718</td>\n",
       "      <td>0.457246</td>\n",
       "      <td>-16.645146</td>\n",
       "      <td>605.933472</td>\n",
       "      <td>0.042416</td>\n",
       "      <td>-1.544076</td>\n",
       "      <td>56.209028</td>\n",
       "      <td>-2046.178007</td>\n",
       "      <td>2072.648112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "      <td>187.553677</td>\n",
       "      <td>98.312514</td>\n",
       "      <td>263.630971</td>\n",
       "      <td>-133.846016</td>\n",
       "      <td>-2.679000</td>\n",
       "      <td>...</td>\n",
       "      <td>-3621.678794</td>\n",
       "      <td>-72.489856</td>\n",
       "      <td>1838.734178</td>\n",
       "      <td>36.803257</td>\n",
       "      <td>0.736637</td>\n",
       "      <td>-933.529330</td>\n",
       "      <td>-18.685094</td>\n",
       "      <td>-0.373992</td>\n",
       "      <td>-0.007486</td>\n",
       "      <td>1701.292666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "      <td>390.726434</td>\n",
       "      <td>218.878557</td>\n",
       "      <td>20.456610</td>\n",
       "      <td>195.477657</td>\n",
       "      <td>1.805316</td>\n",
       "      <td>...</td>\n",
       "      <td>10.591446</td>\n",
       "      <td>0.097816</td>\n",
       "      <td>101.208905</td>\n",
       "      <td>0.934705</td>\n",
       "      <td>0.008632</td>\n",
       "      <td>967.124046</td>\n",
       "      <td>8.931784</td>\n",
       "      <td>0.082489</td>\n",
       "      <td>0.000762</td>\n",
       "      <td>2253.726636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "      <td>28.496841</td>\n",
       "      <td>-71.163840</td>\n",
       "      <td>26.038690</td>\n",
       "      <td>-3.066398</td>\n",
       "      <td>-44.069336</td>\n",
       "      <td>...</td>\n",
       "      <td>13.666955</td>\n",
       "      <td>196.417286</td>\n",
       "      <td>-1.609464</td>\n",
       "      <td>-23.130719</td>\n",
       "      <td>-332.427601</td>\n",
       "      <td>0.189536</td>\n",
       "      <td>2.723946</td>\n",
       "      <td>39.147722</td>\n",
       "      <td>562.619066</td>\n",
       "      <td>486.519017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 56 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5  Feature1^2  \\\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487  238.813659   \n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441  450.364147   \n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619  187.553677   \n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331  390.726434   \n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401   28.496841   \n",
       "\n",
       "   Feature1 Feature2  Feature1 Feature3  Feature1 Feature4  Feature1 Feature5  \\\n",
       "0         275.152347        -371.136432         162.200862          88.433008   \n",
       "1         242.927223         -79.783161          -7.401034         269.419924   \n",
       "2          98.312514         263.630971        -133.846016          -2.679000   \n",
       "3         218.878557          20.456610         195.477657           1.805316   \n",
       "4         -71.163840          26.038690          -3.066398         -44.069336   \n",
       "\n",
       "      ...       Feature3^2 Feature4  Feature3^2 Feature5  Feature3 Feature4^2  \\\n",
       "0     ...              -6053.849078         -3300.599522          2645.764341   \n",
       "1     ...                  4.929117          -179.434718             0.457246   \n",
       "2     ...              -3621.678794           -72.489856          1838.734178   \n",
       "3     ...                 10.591446             0.097816           101.208905   \n",
       "4     ...                 13.666955           196.417286            -1.609464   \n",
       "\n",
       "   Feature3 Feature4 Feature5  Feature3 Feature5^2   Feature4^3  \\\n",
       "0                 1442.488639           786.454576 -1156.300538   \n",
       "1                  -16.645146           605.933472     0.042416   \n",
       "2                   36.803257             0.736637  -933.529330   \n",
       "3                    0.934705             0.008632   967.124046   \n",
       "4                  -23.130719          -332.427601     0.189536   \n",
       "\n",
       "   Feature4^2 Feature5  Feature4 Feature5^2   Feature5^3            y  \n",
       "0          -630.422885          -343.710827  -187.393471  -431.953540  \n",
       "1            -1.544076            56.209028 -2046.178007  2072.648112  \n",
       "2           -18.685094            -0.373992    -0.007486  1701.292666  \n",
       "3             8.931784             0.082489     0.000762  2253.726636  \n",
       "4             2.723946            39.147722   562.619066   486.519017  \n",
       "\n",
       "[5 rows x 56 columns]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_poly['y']=df['y']\n",
    "df_poly.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train=df_poly.drop('y',axis=1)\n",
    "y_train=df_poly['y']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial model without regularization and cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly = LinearRegression(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root-mean-square error of simple polynomial model: 1.89910302223e-11\n"
     ]
    }
   ],
   "source": [
    "model_poly=poly.fit(X_train,y_train)\n",
    "y_poly = poly.predict(X_train)\n",
    "RMSE_poly=np.sqrt(np.sum(np.square(y_poly-y_train)))\n",
    "print(\"Root-mean-square error of simple polynomial model:\",RMSE_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients polynomial model</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature1</th>\n",
       "      <td>1.393774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>11.469286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3</th>\n",
       "      <td>-7.258182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4</th>\n",
       "      <td>4.967388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5</th>\n",
       "      <td>0.428594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2</th>\n",
       "      <td>4.610796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2</th>\n",
       "      <td>0.130565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <td>0.168512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <td>1.652596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <td>0.850184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2</th>\n",
       "      <td>-0.063637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3</th>\n",
       "      <td>1.015700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4</th>\n",
       "      <td>0.112208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature5</th>\n",
       "      <td>1.075431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2</th>\n",
       "      <td>-0.174379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4</th>\n",
       "      <td>0.097619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature5</th>\n",
       "      <td>0.247009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2</th>\n",
       "      <td>-0.361048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5</th>\n",
       "      <td>1.699143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^2</th>\n",
       "      <td>-0.329357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^3</th>\n",
       "      <td>0.004918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature2</th>\n",
       "      <td>0.009731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature3</th>\n",
       "      <td>-0.041778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature4</th>\n",
       "      <td>-0.037414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature5</th>\n",
       "      <td>0.037574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2^2</th>\n",
       "      <td>0.002429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature3</th>\n",
       "      <td>0.038951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature4</th>\n",
       "      <td>-0.016154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature5</th>\n",
       "      <td>-0.003858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3^2</th>\n",
       "      <td>0.101864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3 Feature4</th>\n",
       "      <td>-0.054881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3 Feature5</th>\n",
       "      <td>0.002807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4^2</th>\n",
       "      <td>-0.054250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4 Feature5</th>\n",
       "      <td>0.500361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature5^2</th>\n",
       "      <td>-0.053616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^3</th>\n",
       "      <td>0.025803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature3</th>\n",
       "      <td>0.013705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature4</th>\n",
       "      <td>0.015238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature5</th>\n",
       "      <td>-0.023577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3^2</th>\n",
       "      <td>0.017878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3 Feature4</th>\n",
       "      <td>-0.049529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3 Feature5</th>\n",
       "      <td>0.046253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4^2</th>\n",
       "      <td>-0.086538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4 Feature5</th>\n",
       "      <td>-0.096008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature5^2</th>\n",
       "      <td>0.002131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^3</th>\n",
       "      <td>0.012258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <td>-0.036247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <td>-0.001195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <td>0.007787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <td>0.055605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <td>-0.010458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^3</th>\n",
       "      <td>0.011201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <td>0.120465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <td>0.040685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^3</th>\n",
       "      <td>0.049927</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            Coefficients polynomial model\n",
       "Feature1                                         1.393774\n",
       "Feature2                                        11.469286\n",
       "Feature3                                        -7.258182\n",
       "Feature4                                         4.967388\n",
       "Feature5                                         0.428594\n",
       "Feature1^2                                       4.610796\n",
       "Feature1 Feature2                                0.130565\n",
       "Feature1 Feature3                                0.168512\n",
       "Feature1 Feature4                                1.652596\n",
       "Feature1 Feature5                                0.850184\n",
       "Feature2^2                                      -0.063637\n",
       "Feature2 Feature3                                1.015700\n",
       "Feature2 Feature4                                0.112208\n",
       "Feature2 Feature5                                1.075431\n",
       "Feature3^2                                      -0.174379\n",
       "Feature3 Feature4                                0.097619\n",
       "Feature3 Feature5                                0.247009\n",
       "Feature4^2                                      -0.361048\n",
       "Feature4 Feature5                                1.699143\n",
       "Feature5^2                                      -0.329357\n",
       "Feature1^3                                       0.004918\n",
       "Feature1^2 Feature2                              0.009731\n",
       "Feature1^2 Feature3                             -0.041778\n",
       "Feature1^2 Feature4                             -0.037414\n",
       "Feature1^2 Feature5                              0.037574\n",
       "Feature1 Feature2^2                              0.002429\n",
       "Feature1 Feature2 Feature3                       0.038951\n",
       "Feature1 Feature2 Feature4                      -0.016154\n",
       "Feature1 Feature2 Feature5                      -0.003858\n",
       "Feature1 Feature3^2                              0.101864\n",
       "Feature1 Feature3 Feature4                      -0.054881\n",
       "Feature1 Feature3 Feature5                       0.002807\n",
       "Feature1 Feature4^2                             -0.054250\n",
       "Feature1 Feature4 Feature5                       0.500361\n",
       "Feature1 Feature5^2                             -0.053616\n",
       "Feature2^3                                       0.025803\n",
       "Feature2^2 Feature3                              0.013705\n",
       "Feature2^2 Feature4                              0.015238\n",
       "Feature2^2 Feature5                             -0.023577\n",
       "Feature2 Feature3^2                              0.017878\n",
       "Feature2 Feature3 Feature4                      -0.049529\n",
       "Feature2 Feature3 Feature5                       0.046253\n",
       "Feature2 Feature4^2                             -0.086538\n",
       "Feature2 Feature4 Feature5                      -0.096008\n",
       "Feature2 Feature5^2                              0.002131\n",
       "Feature3^3                                       0.012258\n",
       "Feature3^2 Feature4                             -0.036247\n",
       "Feature3^2 Feature5                             -0.001195\n",
       "Feature3 Feature4^2                              0.007787\n",
       "Feature3 Feature4 Feature5                       0.055605\n",
       "Feature3 Feature5^2                             -0.010458\n",
       "Feature4^3                                       0.011201\n",
       "Feature4^2 Feature5                              0.120465\n",
       "Feature4 Feature5^2                              0.040685\n",
       "Feature5^3                                       0.049927"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff_poly = pd.DataFrame(model_poly.coef_,index=df_poly.drop('y',axis=1).columns, \n",
    "                          columns=['Coefficients polynomial model'])\n",
    "coeff_poly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### R-square value of the simple polynomial model is perfect but the model is flawed as shown above i.e. it learned wrong coefficients and overfitted the to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 value of simple polynomial model: 1.0\n"
     ]
    }
   ],
   "source": [
    "print (\"R2 value of simple polynomial model:\",model_poly.score(X_train,y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metamodel (Optislang style :) - polynomial model with cross-validation and LASSO regularization\n",
    "** This is an advanced machine learning method which prevents over-fitting by penalizing high-valued coefficients i.e. keep them bounded **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LassoCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model1 = LassoCV(cv=10,verbose=0,normalize=True,eps=0.001,n_alphas=100, tol=0.0001,max_iter=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=None, copy_X=True, cv=10, eps=0.001, fit_intercept=True,\n",
       "    max_iter=5000, n_alphas=100, n_jobs=1, normalize=True, positive=False,\n",
       "    precompute='auto', random_state=None, selection='cyclic', tol=0.0001,\n",
       "    verbose=0)"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred1 = np.array(model1.predict(X_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root-mean-square error of Metamodel: 10.6254345131\n"
     ]
    }
   ],
   "source": [
    "RMSE_1=np.sqrt(np.sum(np.square(y_pred1-y_train)))\n",
    "print(\"Root-mean-square error of Metamodel:\",RMSE_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients Metamodel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature1</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>12.891291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2</th>\n",
       "      <td>4.991474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature5</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5</th>\n",
       "      <td>1.995183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature3</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature5</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3^2</th>\n",
       "      <td>0.099441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4^2</th>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4 Feature5</th>\n",
       "      <td>0.799360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature5^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature3</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature4</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4 Feature5</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature5^2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^3</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <td>0.001067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^3</th>\n",
       "      <td>0.099169</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            Coefficients Metamodel\n",
       "Feature1                                  0.000000\n",
       "Feature2                                 12.891291\n",
       "Feature3                                  0.000000\n",
       "Feature4                                  0.000000\n",
       "Feature5                                  0.000000\n",
       "Feature1^2                                4.991474\n",
       "Feature1 Feature2                        -0.000000\n",
       "Feature1 Feature3                         0.000000\n",
       "Feature1 Feature4                         0.000000\n",
       "Feature1 Feature5                         0.000000\n",
       "Feature2^2                                0.000000\n",
       "Feature2 Feature3                         0.000000\n",
       "Feature2 Feature4                        -0.000000\n",
       "Feature2 Feature5                        -0.000000\n",
       "Feature3^2                               -0.000000\n",
       "Feature3 Feature4                         0.000000\n",
       "Feature3 Feature5                         0.000000\n",
       "Feature4^2                                0.000000\n",
       "Feature4 Feature5                         1.995183\n",
       "Feature5^2                               -0.000000\n",
       "Feature1^3                                0.000000\n",
       "Feature1^2 Feature2                       0.000000\n",
       "Feature1^2 Feature3                       0.000000\n",
       "Feature1^2 Feature4                       0.000000\n",
       "Feature1^2 Feature5                       0.000000\n",
       "Feature1 Feature2^2                       0.000000\n",
       "Feature1 Feature2 Feature3               -0.000000\n",
       "Feature1 Feature2 Feature4               -0.000000\n",
       "Feature1 Feature2 Feature5               -0.000000\n",
       "Feature1 Feature3^2                       0.099441\n",
       "Feature1 Feature3 Feature4               -0.000000\n",
       "Feature1 Feature3 Feature5                0.000000\n",
       "Feature1 Feature4^2                       0.000024\n",
       "Feature1 Feature4 Feature5                0.799360\n",
       "Feature1 Feature5^2                       0.000000\n",
       "Feature2^3                                0.000000\n",
       "Feature2^2 Feature3                      -0.000000\n",
       "Feature2^2 Feature4                       0.000000\n",
       "Feature2^2 Feature5                       0.000000\n",
       "Feature2 Feature3^2                       0.000000\n",
       "Feature2 Feature3 Feature4               -0.000000\n",
       "Feature2 Feature3 Feature5                0.000000\n",
       "Feature2 Feature4^2                       0.000000\n",
       "Feature2 Feature4 Feature5               -0.000000\n",
       "Feature2 Feature5^2                      -0.000000\n",
       "Feature3^3                               -0.000000\n",
       "Feature3^2 Feature4                      -0.000000\n",
       "Feature3^2 Feature5                       0.001067\n",
       "Feature3 Feature4^2                       0.000000\n",
       "Feature3 Feature4 Feature5                0.000000\n",
       "Feature3 Feature5^2                      -0.000000\n",
       "Feature4^3                                0.000000\n",
       "Feature4^2 Feature5                       0.000000\n",
       "Feature4 Feature5^2                       0.000000\n",
       "Feature5^3                                0.099169"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff1 = pd.DataFrame(model1.coef_,index=df_poly.drop('y',axis=1).columns, columns=['Coefficients Metamodel'])\n",
    "coeff1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999685404731742"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.score(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11791796322572394"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.alpha_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Recall that the ground  truth  or  originating  function  is  as  follows: \n",
    " \n",
    "$$ y=f(x_1,x_2,x_3,x_4,x_5)= 5x_1^2+13x_2+0.1x_1x_3^2+2x_4x_5+0.1x_5^3+0.8x_1x_4x_5+\\psi(x) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Printing only the non-zero coefficients of the *metamodel*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients Metamodel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>12.891291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2</th>\n",
       "      <td>4.991474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5</th>\n",
       "      <td>1.995183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3^2</th>\n",
       "      <td>0.099441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4^2</th>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4 Feature5</th>\n",
       "      <td>0.799360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <td>0.001067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^3</th>\n",
       "      <td>0.099169</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            Coefficients Metamodel\n",
       "Feature2                                 12.891291\n",
       "Feature1^2                                4.991474\n",
       "Feature4 Feature5                         1.995183\n",
       "Feature1 Feature3^2                       0.099441\n",
       "Feature1 Feature4^2                       0.000024\n",
       "Feature1 Feature4 Feature5                0.799360\n",
       "Feature3^2 Feature5                       0.001067\n",
       "Feature5^3                                0.099169"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff1[coeff1['Coefficients Metamodel']!=0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22998d25588>]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAAHsCAYAAABi/0NiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neRcRERERyRFK3kVEREREcsT/BzdZBixnBH5DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998e798d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel(\"Predicted value with Metamodel\",fontsize=20)\n",
    "plt.ylabel(\"Actual y-values\",fontsize=20)\n",
    "plt.grid(1)\n",
    "plt.scatter(y_pred1,y_train,edgecolors=(0,0,0),lw=2,s=80)\n",
    "plt.plot(y_pred1,y_pred1, 'k--', lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.2215799690947899,\n",
       " 1.0784200309052099,\n",
       " -117815.4824067771,\n",
       " 2474147.0440959162)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaIAAAEKCAYAAABQRFHsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkUKhUCjcilJECoVCoXAr/w8hMoPpETmzrgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998d34080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display results\n",
    "m_log_alphas = -np.log10(model1.alphas_)\n",
    "\n",
    "plt.figure()\n",
    "ymin, ymax = 2300, 3800\n",
    "plt.plot(m_log_alphas, model1.mse_path_, ':')\n",
    "plt.plot(m_log_alphas, model1.mse_path_.mean(axis=-1), 'k',\n",
    "         label='Average across the folds', linewidth=2)\n",
    "plt.axvline(-np.log10(model1.alpha_), linestyle='--', color='k',\n",
    "            label='alpha: CV estimate')\n",
    "plt.legend()\n",
    "\n",
    "plt.xlabel('-log(alpha)')\n",
    "plt.ylabel('Mean square error')\n",
    "plt.axis('tight')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
